hierarchical generalised linear models a synthesis of generalised linear models random effect models and structured dispersions summary hierarchical generalised linear models are developed as a synthesis of generalised linear models mixed linear models and structured dispersions we generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models the method allows models with i any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects ii structured dispersion components iii different link and variance functions for the fixed and random effects and iv the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models inferences can be made by applying standard procedures in particular those for model checking to components of either generalised linear model we also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance likelihood type inference is extended to this wide class of models in a unified way

sensitivity analysis for antenna near field imaging although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results in comparison there are very few results and a limited knowledge about the information content in the inversion data in this paper we provide a mathematical framework for sensitivity analysis of antenna near field imaging problems based on the multipole expansion of the electromagnetic field and the fisher information to quantify the quality of data by exploiting this framework a fundamental relation for accuracy and resolution is formulated based on the crameacuter rao bound crb the sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

the selberg trace formula for bordered riemann surfaces a selberg trace formula is derived for the laplace beltrami operator on bordered riemann surfaces with dirichlet or neumann boundary conditions respectively using a construction via the compact double of the surface for which the standard trace formula is valid applications of the trace formula to spectral functions of the laplace beltrami operators are discussed and their functional determinants are explicitly expressed in terms of various selberg zeta functions for selberg s zeta function relevant to the dirichlet boundary value problem a representation as a dirichlet series is given for which we conjecture conditional convergence even within the critical strip for res 1 2

taylor s power law and fluctuation scaling explained by a central limit like convergence a power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins this taylor s law or fluctuation scaling has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states this hypothesis is predicated on physical quantities like free energy and an external field the correspondence of these quantities with biological systems though remains unproven questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with taylor s law we note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the tweedie exponential dispersion models these latter models are characterized by variance to mean power functions their phenomenological basis rests with a central limit theorem like property that causes many statistical systems to converge mathematically toward a tweedie form we review evaluations of the tweedie poisson gamma model for taylor s law and provide three further cases to test the clustering of single nucleotide polymorphisms snps within the horse chromosome 1 the clustering of genes within human chromosome 8 and the mertens function this latter case is a number theoretic function for which a thermodynamic model cannot explain taylor s law but where tweedie convergence remains applicable the tweedie models are applicable to diverse biological physical and mathematical phenomena that express power variance functions over a wide range of measurement scales they provide a probabilistic description for taylor s law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism

compact isospectral sets of surfaces on etudie des ensembles de surfaces qui sont isospectrales par rapport a l operateur de laplace beltrami

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

robust inference in the negative binomial regression model with an application to falls data summary a popular way to model overdispersed count data such as the number of falls reported during intervention studies is by means of the negative binomial nb distribution classical estimating methods are well known to be sensitive to model misspecifications taking the form of patients falling much more than expected in such intervention studies where the nb regression model is used we extend in this article two approaches for building robust m estimators of the regression parameters in the class of generalized linear models to the nb distribution the first approach achieves robustness in the response by applying a bounded function on the pearson residuals arising in the maximum likelihood estimating equations while the second approach achieves robustness by bounding the unscaled deviance components for both approaches we explore different choices for the bounding functions through a unified notation we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately and provide the asymptotic distributions of the resulting estimators moreover we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter specific to the nb distribution simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model and this for both approaches we present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

estimation of the negative binomial parameter κ by maximum quasi likelihood we investigate estimation of the parameter k of the negative binomial distribution for small samples using a method of moments estimate mme and a maximum quasi likelihood estimate mqle previous work is reviewed the importance of indirect estimation of k through its reciprocal a and of allowance for negative estimates of k or a are discussed samples of size 50 are simulated 10 000 times for each of several parameter combinations to examine the properties of the estimates samples of sizes 10 20 30 and 50 are simulated 1 000 times to investigate the effect of sample size both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20 three examples are given one of a designed experiment for which the mqle is especially suited confidence limits are derived for the mqle further work along these lines is required for adequate assessment of the usual maximum likelihood estimate

identifiability of factor analysis some results and open problems abstract identifiability of the factor analysis model is discussed and some recent results and their relation to previous work are surveyed sufficient conditions for local identifiability are presented a counterexample shows that these conditions are not necessary in general a simple counting rule for local identifiability of the factor analysis model is given generically finally some open problems are formulated

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

extended moment series and the parameters of the negative binomial distribution recent studies indicate that for finite sample sizes moment estimators may be superior to maximum likelihood estimators in some regions of parameter space in this paper a statistic based on the central moment of the sample is expanded in a taylor series using 24 derivatives and many more terms than previous expansions a summary algorithm is required to find meaningful approximants using the higher order coefficients a example is presented and a comparison between theoretical assessment and simulation results is made

complex factor analysis and extensions many subspace based array signal processing algorithms assume that the noise is spatially white in this case the noise covariance matrix is a multiple of the identity and the eigenvectors of the data covariance matrix are not affected by it if the noise covariance is an unknown arbitrary diagonal e g for an uncalibrated array the eigenvalue decomposition leads to incorrect subspace estimates and it has to be replaced by a more general factor analysis decomposition fa which then reveals all relevant information we consider this data model and several extensions where the noise covariance matrix has a more general structure such as banded sparse block diagonal and cases where we have multiple data covariance matrices that share the same noise covariance matrix starting from a nonlinear weighted least squares formulation we propose new estimation algorithms for both classical fa and its extensions the optimization is based on gauss newton gradient descent generally this leads to an iteration involving the inversion of a very large matrix using the structure of the problem we show how this can be reduced to the inversion of a matrix with dimension equal to the number of unknown noise covariance parameters this results in new algorithms that have faster numerical convergence and lower complexity compared to several maximum likelihood based algorithms that could be considered state of the art the new algorithms scale well to large dimensions and can replace eigenvalue decompositions in many applications even if the noise can be assumed to be white

weighted minimum trace factor analysis in the last decade several authors discussed the so called minimum trace factor analysis mtfa which provides the greatest lower bound g l b to reliability however the mtfa fails to be scale free in this paper we propose to solve the scale problem by maximization of the g l b as the function of weights closely related to the primal problem of the g l b maximization is the dual problem we investigate the primal and dual problems utilizing convex analysis techniques the asymptotic distribution of the maximal g l b is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions finally we outline computational algorithms and consider numerical examples

a conditional likelihood approach to residual maximum likelihood estimation in generalized linear models summary residual maximum likelihood reml estimation is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters in this paper it is shown that reml has an exact conditional likelihood interpretation where the conditioning is on an appropriate sufficient statistic to remove dependence on the nuisance parameters this interpretation clarifies the motivation for reml and generalizes directly to non normal models in which there is a low dimensional sufficient statistic for the fitted values the conditional likelihood is shown to be well defined and to satisfy the properties of a likelihood function even though this is not generally true when conditioning on statistics which depend on parameters of interest using the conditional likelihood representation the concept of reml is extended to generalized linear models with varying dispersion and canonical link explicit calculation of the conditional likelihood is given for the one way lay out a saddlepoint approximation for the conditional likelihood is also derived

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

bias corrected maximum likelihood estimator of the negative binomial dispersion parameter nous decrivons un estimateur du maximum de vraisemblance avec correction du premier ordre pour le biais sur le parametre de dispersion d une distribution binomiale negative cet estimateur est compare en terme debiais et d efficacite avec l estimateur du maximum de vraisemblance etudie par piegorsch 1990 biometrics 46 863 867 les estimateurs de moment et du maximum de quasi vraisemblance etendue de clark et perry 1989 biometrics 45 309 316 et un estimateur de double quasi vraisemblance etendue l estimateur du maximum de vraisemblance avec correction du biais a des proprietes de biais et d efficacite superieures dans la plupart des cas pour faciliter la comparaison nous donnons les resultats pour le modele binomial negatif a deux parametres cependant un exemple impliquant la regression binomiale negative est donne

maximum likelihood estimation for array processing in colored noise direction of arrival estimation of multiple sources using a uniform linear array in noise with unknown covariance is considered the noise is modeled as a spatial autoregressive process with unknown parameters both stochastic and deterministic signal models are considered for the random signal case an approximate maximum likelihood estimator of the signal and noise parameters is derived it requires numerical maximization of a compressed likelihood function over the unknown arrival angles analytical expressions for the mles of the signal covariance and the ar parameters are given similar results for the case of deterministic signals are also presented

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

asymptotics of the spectrum and the selberg zeta function on the space of riemann surfaces letz s r be the selberg zeta function of a compact riemann surfacer we study the behavior ofz s r asr tends to infinity in the moduli space of stable curves the main result is an estimate forz s r valid fors in a neighborhood depending only on the genus ofs 1 our analysis gives an alternate proof of the belavin knizhnik double pole result 5

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

similarity indices for spatia i ecological data summary we present a method for assessing similarity between species maps of presence and absence or abundance that emphasizes global features while ignoring minor local dissimilarities the method arranges sites into small groups or cliques and allows controlled changes to be made within cliques to reduce the influence of local discrepancies resulting measures of similarity are visually more satisfactory than traditional indices we show that the similarity indices are useful for model selection by comparing observed spatial patterns with those predicted by different fitted models examples are provided for spatial distributions of oribatid mites acari oribatei woodlarks lullula arborea and red deer genius elaphus

maximum likelihood bearing estimation with partly calibrated arrays in spatially correlated noise fields the problem of using a partly calibrated array for maximum likelihood ml bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions more exactly this paper assumes that the array contains some calibrated sensors whose number is only required to be larger than the number of signals impinging on the array and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors these two noise vectors however may have arbitrary spatial autocovariance matrices under these assumptions the many nuisance parameters viz the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors can be eliminated from the likelihood function leaving a significantly simplified concentrated likelihood whose maximum yields the ml bearing estimates the ml estimator introduced in this paper and referred to as mle is shown to be asymptotically equivalent to a recently proposed subspace based bearing estimator called uncle and rederived herein by a much simpler approach than in the original work a statistical analysis derives the asymptotic distribution of the mle and uncle estimates and proves that they are asymptotically equivalent and statistically efficient in a simulation study the mle and uncle methods are found to possess very similar finite sample properties as well as uncle is computationally more efficient it may be the preferred technique in a given application

families of distributions for repeated samples of animal counts the criterion of flexibility perry and taylor 1985 journal of animal ecology 54 931 953 that families of distributions with n 2 parameters should fit adequately to all n samples of animal counts over the full range of population densities usually encountered was misinterpreted by kemp 1987 biometrics 43 693 699 this criterion of goodness of fit is examined here for perry and taylor s ades family and one of kemp s alternatives a family of constrained negative binomial c n b distributions using extensive literature data while the ades fitted better than the c n b in 15 of 22 sets the evidence is not overwhelming because in 13 sets the difference was negligible or both families fitted adequately however of the remainder the ades fitted notably better to seven sets these mainly comprised long tailed distributions with large means typical of pest species its use in practical applications with such data is discussed and the importance of its superior reliability stressed kemp s method of fitting is not recommended

minres qlp a krylov subspace method for indefinite or singular symmetric systems cg symmlq and minres are krylov subspace methods for solving symmetric systems of linear equations when these methods are applied to an incompatible system that is a singular symmetric least squares problem cg could break down and symmlq s solution could explode while minres would give a least squares solution but not necessarily the minimum length pseudoinverse solution this understanding motivates us to design a minres like algorithm to compute minimum length solutions to singular symmetric systems minres uses qr factors of the tridiagonal matrix from the lanczos process where r is upper tridiagonal minres qlp uses a qlp decomposition where rotations on the right reduce r to lower tridiagonal form on ill conditioned systems singular or not minres qlp can give more accurate solutions than minres we derive preconditioned minres qlp new stopping rules and better estimates of the solution and residual norms the matrix norm and the condition number

maximum likelihood estimation for the negative binomial dispersion parameter a 2 this yf y k for k 0 u 0 anscombe 1950 here u e y and k 1 a also var y u a2 k a aa2 this distribution has numerous applications in the biological sciences see e g breslow 1984 margolin kim and risko 1989 and the references in clark and perry 1989 anscombe 1950 observed that strictly speaking the maximum likelihood ml estimator of k k does not have a distribution since there exists a finite probability of observing a data set from which k may not be calculated this occurs when the sample mean exceeds the sample variance a more useful parameterization involves a 1 k giving

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

diversity as a concept and its measurement abstract this paper puts forth the view that diversity is an average property of a community and identifies that property as species rarity an intrinsic diversity ordering of communities is defined and is shown to be equivalent to stochastic ordering also the sensitivity of an index to rare species is developed culminating in a crossing point theorem and a response theory to perturbations diversity decompositions analogous to the analysis of variance are discussed for two way classifications and mixtures the paper concludes with a brief survey of genetic diversity linguistic diversity industrial concentration and income inequality

estimation of the shape parameter k of the negative binomial distribution using approximate bayesian methods an estimator of the shape parameter of the negative binomial distribution is introduced most of the available estimators of this parameter such as the method of moment and the maximum likelihood estimators mme and mle give inadmissible values when the mean of the observed sample is larger than its variance in this case the mme gives values while the mle is infinite such observed sample in not unlikely when the mean of the population is close to its variance the suggested estimator always has valid values and turned out to be more efficient for most values of the parameter space family size data is used for illustration of the procedure

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

surfaces with boundary their uniformizations determinants of laplacians and isospectrality let be a compact surface of type g n n 0 obtained by re moving n disjoint disks from a closed surface of genus g assuming 0 while osgood phillips and sarnak o p s3 showed the properness when g 0

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis one of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries we show in this paper that the set of matrices which can be reduced to rankr has positive lebesgue measure if and only ifr is greater or equal to the ledermann bound in other words the ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix afterwards an asymptotic sampling theory of so called minimum trace factor analysis mtfa is proposed the theory is based on continuous and differential properties of functions involved in the mtfa convex analysis techniques are utilized to obtain conditions for differentiability of these functions

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

detection and localization in colored noise via generalized least squares a method for detection and localization of multiple signals in spatially colored noise by an arbitrary passive sensor array is presented the method also enables exploitation of prior knowledge that the signals are uncorrelated so as to improve the performance and to allow detection and localization even if the number of signals exceeds the number of sensors the estimation based on the generalized least squares criterion is both consistent and asymptotically efficient the detection is performed via the minimum description length mdl principle and is proved to be consistent simulation results confirming the theoretical results are included

moduli space heights and isospectral sets of plane domains let q be a plane domain of finite connectivity n with smooth boundary and choose a fixed domain 2 of the same type then there exists a flat metric g on 2 such that q is isometric with 29g in what follows we do not distinguish between isometric domains by the spectrum of 29 we mean the spectrum of the laplace beltrami operator ag on 29 with dirichlet boundary conditions the height h eg log det ag is a spectral invariant and plays a central role in this paper among all suitably normalized flat metrics on 2 conformal to a given metric g there is a unique flat metric for which the height is a minimum this metric is characterized by the fact that d 2 has constant geodesic curvature we call such a metric uniform and denote it by u the set of all such metrics is denoted by u 2 we can therefore identify with the moduli space 2 of conformal structures on e for n 3 we introduce a special parametrization for mu 2 by means of which we show that h u oo as u approaches the boundary of fu 2 using this along with the heat invariants for the laplacian we then show that any isospectral set of plane domains is compact in the c topology similar results hold for n 1 and 2

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

families of discrete distributions satisfying taylor s power law count data in entomological studies can often be described by some form of contagious distribution such as the negative binomial neyman type a or polya aeppli these are all clustered poisson distributions their distributional forms are given in section 2 arising when groups of individuals occur at random i e are poissonian and individuals within a group have their own distribution whilst pahl 1969 found strong evidence that the negative binomial distribution gives good fits to his 35 samples of data on the chrysomelid beetle paropsis atomaria martin and katti 1965 fitted a number of distributions to a variety of insect plant and animal data and observed for instance that mcguire brindley and bancroft s 1957 data on the european cornborer pyrausta nubilalis and beall s 1940 data on the beet webworm loxostege sticticalis are fitted well not only by the negative binomial but also by the neyman type a and other distributions in such circumstances the fits given by different distributions are often very similar and the exact choice is not critical see kemp and kemp 1965 the recent work of tripathi gurland and bhalerao 1986 gives further guidance on the choice of an appropriate distribution when this is not clearly indicated by the ecological context the negative binomial neyman type a and polya aeppli distributions all have two parameters when there are many samples of data in one data set anscombe 1949 and bliss and owen 1958 suggested fitting a model that is parsimonious in parameters by keeping one of them constant from sample to sample their use of a common exponent parameter k when fitting families of negative binomials was criticised by taylor woiwod and perry 1979 who considered that k is an unstable parameter whose relationship with aggregation is doubtful much empirical evidence has accumulated in support of taylor s power law

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

a new index of aggregation for animal counts a new index is described that is especially appropriate for measuring the aggregation of entomological data in the form of counts per sample unit and that can make use of spatial information when it is available calculation of the index is based on a comparison of the effort required of individuals in a sample to achieve complete crowding with that to achieve complete randomness the power of tests of randomness based on this index is found to be greater than those based on the index of dispersion especially when spatial information is available

multistage estimation compared with fixed sample size estimation of the negative binomial parameter k the negative binomial distribution often fits biological data well since the mean is of primary interest the parameterization in terms of the mean and a parameter k has become almost standard given a precise estimate of k sequential methods of estimating the mean are available however precise estimation of k has been elusive in this paper estimators of k by the method of moments and by maximum likelihood estimation based on samples of size 50 and 100 are investigated by using monte carlo methods although the maximum likelihood estimators tend to have smaller mean square errors than the method of moments estimators neither can be considered good a multistage approach to the estimation of k is presented and monte carlo results indicate that this procedure gives a mean square error less than that of comparable fixed sample size estimators two truncation rules for the multistage procedure are also given and compared

fitting the negative binomial distribution this note is a reaction to recent papers in this journal by willson folks and young 1984 and bowman 1984 for the biometrical analysis of certain kinds of observations such as insect counts accident counts or cave entrance counts when only nonnegative integers are observable it is expedient to restrict attention to those random variables which are restricted to the lattice of nonnegative integers cf noack 1950 with an admitted loss of generality one may substantially simplify the procedure by a further restriction using as a frame of reference the family of binomial frequency functions hoel 1947 within this frame of reference the use of the modem restatement of the time honored occam s razor principle wrinch and jeffreys 1921 quoted by popper 1959 p 171 leads rather straightforwardly to a null hypothesis which may be discussed expediently in terms of the number n of distinct but not necessarily all unequal observations rj of r j 1 n writing

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

distributional properties of the number of moves index of diversity the large sample distribution of the number of moves index of diversity is shown to be approximately normal under the general assumption of asymptotic normality of the species frequencies its distribution can be fit by the beta distribution for completely even underlying populations exact smallsample moments are computed assuming multinomial frequencies with an equiprobable and a broken stick model the scaled version of the index appears to be biased upward for small samples from uneven populations when the number of species in the population is unknown an application is illustrated for comparing the population diversities of the prey consumed by white crappie at different lake depths

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions