unbounded perturbation of the exponential dichotomy for evolution equations abstract in this paper we prove that the exponential dichotomy for evolution equations in banach spaces is not destroyed if we perturb the equation by small unbounded linear operator this is done by employing a skew product semiflow technique and a perturbation principle from linear operator theory finally we apply these results to partial parabolic equations and functional differential equations

bias reduction in exponential family nonlinear models in firth 1993 biometrika it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector and that in canonical link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data here a more general family of bias reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models the resulting formulae for the adjusted score vector are computationally convenient and in univariate models they directly suggest implementation through an iterative scheme of data adjustment for generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method an illustrative application to the goodman row column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models

the effect of bias variance estimation skewness and kurtosis of the empirical logit on weighted least squares analyses summary the bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation the covariance of the empirical logit and its estimated variance is derived neither the 2 correction of haldane 1955 and anscombe 1956 nor the 2 suggested by cox 1970 for weighted logit regression is universally effective in reducing bias other corrections are considered the distribution of the empirical logit is shown to be considerably more skewed and to have a much larger kurtosis than the comparable binomial distribution methods based directly on sufficient statistics are preferred to those based on the empirical logit

fredholm differential operators with unbounded coefficients abstract we prove that a first order linear differential operator g with unbounded operator coefficients is fredholm on spaces of functions on r with values in a reflexive banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both r and r and a pair of the ranges of the dichotomy projections is fredholm and that the fredholm index of g is equal to the fredholm index of the pair the operator g is the generator of the evolution semigroup associated with the evolution family in the case when the evolution family is the propagator of a well posed differential equation u t a t u t with generally unbounded operators a t t r the operator g is a closure of the operator d dt a t thus this paper provides a complete infinite dimensional generalization of well known finite dimensional results by palmer and by ben artzi and gohberg

estimating latent processes on a network from indirect measurements in a communication network point to point traffic volumes over time are critical for designing protocols that route information efficiently and for maintaining security whether at the scale of an internet service provider or within a corporation while technically feasible the direct measurement of point to point traffic imposes a heavy burden on network performance and is typically not implemented instead indirect aggregate traffic volumes are routinely collected we consider the problem of estimating point to point traffic volumes from aggregate traffic volumes given information about the network routing protocol encoded in a matrix a this estimation task can be reformulated as finding the solutions to a sequence of ill posed linear inverse problems since the number of origin destination routes of interest is higher than the number of aggregate measurements available here we introduce a novel multilevel state space model ssm of aggregate traffic volumes with realistic features we imp

quasi hyperbolic semigroups abstract we introduce the notion of quasi hyperbolic operators and c 0 semigroups examples include the push forward operator associated with a quasi anosov diffeomorphism or flow a quasi hyperbolic operator can be characterised by a simple spectral property or as the restriction of a hyperbolic operator to an invariant subspace there is a corresponding spectral property for the generator of a c 0 semigroup and it characterises quasi hyperbolicity on hilbert spaces but not on other banach spaces we exhibit some weaker properties which are implied by the spectral property

multiple imputation when records used for imputation are not used or disseminated for analysis summary when some of the records used to estimate the imputation models in multiple imputation are not used or available for analysis the usual multiple imputation variance estimator has positive bias we present an alternative approach that enables unbiased estimation of variances and hence calibrated inferences in such contexts first using all records the imputer samples m values of the parameters of the imputation model second for each parameter draw the imputer simulates the missing values for all records n times from these mn completed datasets the imputer can analyse or disseminate the appropriate subset of records we develop methods for interval estima tion and significance testing for this approach methods are presented in the context of multiple imputation for measurement error

a note on multiple imputation for method of moments estimation multiple imputation is a popular imputation method for general purpose estimation rubin 1987 provided an easily applicable formula for the variance estimation of multiple imputation however the validity of the multiple imputation inference requires the congeniality condition of meng 1994 which is not necessarily satisfied for method of moments estimation this paper presents the asymptotic bias of rubin s variance estimator when the method of moments estimator is used as a complete sample estimator in the multiple imputation procedure a new variance estimator based on over imputation is proposed to provide asymptotically valid inference for method of moments estimation

strong stability of bounded evolution families and semigroups abstract we prove several characterizations of strong stability of uniformly bounded evolution families u t s t s 0 of bounded operators on a banach space x i e we characterize the property lim t u t s x 0 for all s 0 and all x x these results are connected to the asymptotic stability of the well posed linear nonautonomous cauchy problem u t a t u t t s 0 u s x x x in the autonomous case i e when u t s t t s for some c 0 semigroup t t t 0 we present in addition a range condition on the generator a of t t t 0 which is sufficient for strong stability this condition is more general than the condition in the ablv theorem involving countability of the imaginary part of the spectrum of a

an empirical bayes estimator for in scale adaptive filtering a scale adaptive filtering scheme is developed for underspread channels based on a model of the linear time varying channel operator as a process in scale recursions serve the purpose of adding detail to the filter estimate until a suitable measure of fidelity and complexity is met resolution of the channel impulse response associated with its coherence time is naturally modeled over the observation time via a gaussian mixture assignment on wavelet coefficients maximum likelihood approximate maximum a posteriori map and posterior mean estimators as well as associated variances are derived doppler spread estimation associated with the coherence time of the filter is synonymous with model order selection and a map estimate is presented and compared with laplace s approximation and the popular aic the algorithm is implemented with conjugate gradient iterations at each scale and as the coherence time is recursively decreased the lower scale estimate serves as a starting point for successive reduced coherence time estimates the algorithm is applied to a set of simulated sparse multipath doppler spread channels demonstrating the superior mse performance of the posterior mean filter estimator and the superiority of the map doppler spread stopping rule

confidence intervals for multinomial logistic regression in sparse data logistic regression is one of the most widely used regression models in practice but alternatives to conventional maximum likelihood estimation methods may be more appropriate for small or sparse samples modification of the logistic regression score function to remove first order bias is equivalent to penalizing the likelihood by the jeffreys prior and yields penalized maximum likelihood estimates ples that always exist even in samples in which maximum likelihood estimates mles are infinite ples are an attractive alternative in small to moderate sized samples and are preferred to exact conditional mles when there are continuous covariates we present methods to construct confidence intervals ci in the penalized multinomial logistic regression model and compare ci coverage and length for the ple based methods to that of conventional mle based methods in trinomial logistic regressions with both binary and continuous covariates based on simulation studies in sparse data sets we recommend profile cis over asymptotic wald type intervals for the ples in all cases furthermore when finite sample bias and data separation are likely to occur we prefer ple profile cis over mle methods

persistence and imperfection of nonautonomous bifurcation patterns abstract for nonautonomous dynamical systems a bifurcation can be understood as topological change in the set of bounded entire solutions to a given time dependent evolutionary equation following this idea a fredholm theory via exponential dichotomies on semiaxes enables us to employ tools from analytical branching theory yielding nonautonomous versions of fold transcritical and pitchfork patterns this approach imposes the serious hypothesis that precise quantitative information on the dichotomies is required an assumption hard to satisfy in applications thus imperfect bifurcations become important in this paper we discuss persistence and changes in the previously mentioned bifurcation scenarios by including an additional perturbation parameter while the unperturbed case captures the above bifurcation patterns we obtain their unfolding and therefore the local branching picture in a whole neighborhood of the system using an operator formulation of parabolic differential caratheodory differential and difference equations this will be achieved on the basis of recent abstract analytical techniques due to shi 1999 and liu shi and wang 2007

equivalences between nonuniform exponential dichotomy and admissibility abstract relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems it was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy in this paper we find an appropriate admissible pair of classes of lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half lines r separately on both half lines r simultaneously and on the whole line r additionally the maximal admissibility is proved in the case on both half lines r simultaneously

constrained and preconditioned stochastic gradient method we consider stochastic approximations that arise from such applications as data communications and image processing we demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be incorporated into a preconditioning technique to derive the preconditioned stochastic gradient method psgm we perform convergence analysis to show that the psgm converges to the theoretical best approximation under some simple assumptions on the preconditioner and on the independence of samples drawn from a stochastic process simulation results are presented to demonstrate the effectiveness of the constrained and preconditioned stochastic gradient method

analysis of conjugate gradient algorithms for adaptive filtering the paper presents and analyzes two approaches to the implementation of the conjugate gradient cg algorithm for filtering where several modifications to the original cg method are proposed the convergence rates and misadjustments for the two approaches are compared an analysis in the z domain is used in order to find the asymptotic performance and stability bounds are established the behavior of the algorithms in finite word length computation are described and dynamic range considerations are discussed it is shown that in finite word length computation and close to steady state the algorithms behaviors are similar to the steepest descent algorithm where the stalling phenomenon is observed using 16 bit fixed point number representation our simulations show that the algorithms are numerically stable

robust adaptive beamforming based on conjugate gradient algorithms the mismatches of signal and array geometry will seriously degrade the performance of adaptive beamformer in this paper we propose two methods for robust adaptive beamforming based on the conjugate gradient cg algorithm the proposed beamformers offer a significant improvement in the computational complexity while providing the same performance of the best robust beamformers at present the first method belongs to the diagonal loading technique we derive a diagonal loading cgls algorithm cg applied to normal equations and propose a simple method to choose the loading level based on a coarse estimation of the desired signal power this parameter free method can effectively reduce the signal self cancellation at high signal to noise ratio the second method belongs to the regularization technique since the cg algorithm has a regularizing effect with iteration number being the regularization parameter the stopping criterion plays an important role on the robustness we develop three fast stopping criteria for cg iteration which reduce the stopping complexity from o n or o n 2 to o 1 the former two are the fast versions of existing methods and the later one is new moreover the new criterion based on fast ritz value estimation has better performance than others

exponential dichotomy and lp lq admissibility on the half line abstract we give necessary and sufficient conditions for uniform exponential dichotomy of discrete evolution families in terms of the admissibility of the pair l p n x l 0 q n x we prove that the admissibility of the pair l p n x l 0 q n x is a sufficient condition for uniform exponential dichotomy of a discrete evolution family this condition becomes necessary for discrete evolution families with uniform exponential growth if and only if p q as consequences we obtain necessary and sufficient conditions for uniform exponential dichotomy of evolution families

conjugate gradient eigenstructure tracking for adaptive spectral estimation a conjugate gradient iteration is derived that converges to the set of r dominant subdominant eigenpairs this iteration is used to construct two eigenstructure tracking algorithms that track the r dimensional dominant or subdominant subspaces of time varying data or data covariance matrices the two eigenstructure tracking algorithms have update complexities o m sup 2 r and the other o mr sup 2 where m is the data dimension the algorithms are customized to solve high resolution temporal and spatial frequency tracking problems they are compared with existing techniques by tying into published simulation based performance tests the algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost

bayesian nonparametric multiple imputation of partially observed data with ignorable nonresponse summary we present a new nonparametric bayesian method for multiple imputation of partially observed data for which the pattern of missingness is arbitrary and the data are missing at random with ignorable nonresponse with respect to the model specification motivation for the method is provided followed by an overview of p61lya trees and their application to multiple imputation and a comparison of the new method to existing approaches is presented the method is illustrated on a dataset of colleges and universities in the united states partially observed information frequently occurs in the analysis of multivariate data often resulting in an arbitrary pattern of missingness a popular method for modelling such data is multiple imputation which entails specifying a probability model for the parameters of interest and the missing data the missing data are treated as unknown quantities which are to be estimated and the posterior distributions of the model parameters of interest are obtained by marginalising over the uncertainty induced by the missing data in practice multiple imputation is implemented by simulating m copies of the missing data combining each copy of the missing data with the observed data to yield an estimate of the parameters of interest and combining the resulting m estimates to create one final estimate rubin 1987 ch 3 in contrast to the case with alternative methods the variances of estimated parameters based on multiply imputed and observed data can be correctly estimated provided necessary assumptions are met rubin 1987 ch 4 meng 1994

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

on the bias of the multiple imputation variance estimator in survey sampling summary multiple imputation is a method of estimating the variances of estimators that are constructed with some imputed data we give an expression for the bias of the multiple imputation variance estimator for data that are collected with a complex sample design the bias may be sizable for certain estimators such as domain means when a large fraction of the values are imputed a bias adjusted variance estimator is suggested

characterizations of dichotomies of evolution equations on the half line abstract in this paper we investigate the characterization of dichotomies of an evolution family u u t s t s 0 of bounded linear operators on banach space x we introduce operators i0 and ix on subspaces of lp r x using the integral equation u t u t s u s ts u t f d the exponential and ordinary dichotomies of u are characterized by properties of i0 ix

exponential dichotomies and homoclinic orbits in functional differential equations abstract suppose an autonomous functional differential equation has an orbit which is homoclinic to a hyperbolic equilibrium point the purpose of this paper is to give a procedure for determining the behavior of the solutions near of a functional differential equation which is a nonautonomous periodic perturbation of the original one the procedure uses exponential dichotomies and the fredholm alternative it is also shown that any smooth function p t defined on the reals which approaches zero monotonically as t is the solution of a scalar functional differential equation and generates an orbit homoclinic to zero examples illustrating the results are also given

nonuniform h k μ ν dichotomy with applications to nonautonomous dynamical systems the paper develops and studies a very general notion of dichotomy referred to as nonuniform h k dichotomy the new notion contains as special cases most versions of dichotomy existing in the literature the paper then provides corresponding new versions of robustness hartman grobman theorem and stable manifold theorem for nonautonomous dynamical systems in banach spaces in term of the nonuniform h k dichotomy

admissibility and roughness of nonuniform exponential dichotomies for difference equations abstract in this paper we discuss on relationships between nonuniform exponential dichotomies of nonautonomous difference equations and admissibility for classes of weighted bounded solutions and show the roughness of nonuniform exponential dichotomies in the finite dimensional case we give sufficient conditions for existence of nonuniform exponential dichotomies on z 0 or z 0 separately on z 0 and z 0 simultaneously and on the whole z as an application we use this result to discuss the roughness of nonuniform exponential dichotomies for difference equations on z 0 z 0 and the whole z separately and obtain better estimates for both the bound and the nonuniformity degree

estimating heterogeneity in the probabilities of enumeration for dual system estimation abstract we show how conditional logistic regression can be used to estimate the probability of being enumerated in a census and apply the model to the 1990 post enumeration survey pes in the united states the estimates can be used in the estimation of population size and the estimation of correlation bias for example unlike the classical stratification approach the logistic approach permits the use of continuous explanatory variables model choice can be based on the standard techniques of the generalized linear models we discuss some special problems caused by the fact that the pes sample area is open to migration between the captures we also consider the effect of data errors in estimation we characterize hard to enumerate populations and give some tentative estimates of correlation bias

low complexity rls algorithms using dichotomous coordinate descent iterations in this paper we derive low complexity recursive least squares rls adaptive filtering algorithms we express the rls problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new rls techniques for solving the auxiliary equations line search methods are used we first consider conjugate gradient iterations with a complexity of operations per sample being the number of the filter weights to reduce the complexity and make the algorithms more suitable for finite precision implementation we propose a new dichotomous coordinate descent dcd algorithm and apply it to the auxiliary equations this results in a transversal rls adaptive filter with complexity as low as multiplications per sample which is only slightly higher than the complexity of the least mean squares lms algorithm multiplications simulations are used to compare the performance of the proposed algorithms against the classical rls and known advanced adaptive algorithms fixed point fpga implementation of the proposed dcd based rls algorithm is also discussed and results of such implementation are presented

conjugate gradient method in adaptive bilinear filtering the application of the conjugate gradient cg method for the identification of bilinear systems is investigated an algorithm based on the cg method is developed for adaptive bilinear digital filtering in this algorithm the optimization is done over blocks of input and output data rather than a single pair of data however only one iteration and coefficient update is done for every sample of data this coupled with the fact that the cg method used does not require a line search makes it very efficient in computation simulation results show that this algorithm outperforms the lms and rls algorithms in terms of speed of convergence a preconditioning technique is also applied to further accelerate the convergence in some cases

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

the fredholm alternative for parabolic evolution equations with inhomogeneous boundary conditions abstract we study the fredholm properties of parabolic evolution equations on r with inhomogeneous boundary values these problems are transformed into evolution equations with inhomogeneities taking values in certain extrapolation spaces assuming that the underlying homogeneous problem is asymptotically hyperbolic we show the fredholm alternative for these equations the results are applied to parabolic partial differential equations

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

blocked designs for experiments with correlated non normal response many experiments measure a response that cannot be adequately described by a linear model with normally distributed errors and are often run in blocks of homogeneous experimental units we develop the first general methods of obtaining efficient blocked designs for experiments with an exponential family response described by a marginal model fitted via generalized estimating equations this methodology is appropriate when the blocking factor is a nuisance variable as often occurs in industrial experiments a d optimality criterion is developed for finding designs robust to the values of the marginal model parameters and applied using two strategies unrestricted algorithmic search and blocking of an optimal design for the corresponding generalized linear model glm designs from each strategy are critically compared and shown to be more efficient than use of a random allocation to blocks of the points from an optimal glm design the designs are compared for a range of values of the intra block working c

on the conjugate gradient matched filter the conjugate gradient cg algorithm is an efficient method for the calculation of the weight vector of the matched filter mf as an iterative algorithm it produces a series of approximations to the mf weight vector each of which can be used to filter the test signal and form a test statistic this effectively leads to a family of detectors referred to as the cg mf detectors which are indexed by the number of iterations incurred we first consider a general case involving an arbitrary covariance matrix of the disturbance including interference noise etc and show that all cg mf detectors attain constant false alarm rate cfar and furthermore are optimum in the sense that the th cg mf detector yields the highest output signal to interference and noise ratio sinr among all linear detectors within the th krylov subspace we then consider a structured case frequently encountered in practice where the covariance matrix of the disturbance contains a low rank component rank due to dominant interference sources a scaled identity due to the presence of a white noise and a perturbation component containing the residual interference we show that the st cg mf detector achieves cfar and an output sinr nearly identical to that of the mf detector which requires complete iterations of the cg algorithm till reaching convergence hence the st cg mf detector can be used in place of the mf detector for significant computational saving when is small numerical results are presented to verify the accuracy of our analysis for the cg mf detectors

the fredholm alternative and exponential dichotomies for parabolic equations abstract it is proved in this paper for parabolic equations that the fredholm alternative holds for bounded solutions if the homogeneous equation has exponential dichotomies on r and on r and moreover that the converse is also valid under the condition of bounded growth

models for categorical data with nonignorable nonresponse abstract when categorical outcomes are subject to nonignorable nonresponse log linear models may be used to adjust for the nonresponse the models are fitted to the data in an augmented frequency table in which one index corresponds to whether or not the subject is a respondent the likelihood function is maximized over pseudo observed cell frequencies with respect to this log linear model using an em algorithm each e step of the em algorithm determines the pseudo observed cell frequencies and the m step yields the maximum likelihood estimators mle s of these pseudo observed cell frequencies this approach may produce boundary estimates for the expected cell frequencies of the nonrespondents in these cases the estimators of the log linear model parameters are not uniquely determined and may be unstable following the approach of clogg et al we propose a bayesian method that uses smoothing constants to adjust the pseudo observed cell frequencies so that the solution is not on the boundary the role

adaptive conjugate gradient dfes for wideband mimo systems new adaptive equalization algorithms for wireless systems operating over wideband multiple input multiple output mimo channels are proposed the problem of mimo decision feedback equalizer dfe design is formulated as a set of linear equations with multiple right hand sides rhss evolving in time by applying an adaptive modified conjugate gradient algorithm we derive an equalizer with identical convergence improved tracking capabilities but higher computational load as compared to the recursive least squares rls algorithm to reduce its complexity two updating strategies of the equalizer filters based on galerkin projections are employed

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

reduced rank stap schemes for airborne radar based on switched joint interpolation decimation and filtering algorithm in this paper we propose a reduced rank space time adaptive processing stap technique for airborne phased array radar applications the proposed stap method performs dimensionality reduction by using a reduced rank switched joint interpolation decimation and filtering algorithm rr sjidf in this scheme a multiple processing branch mpb framework which contains a set of jointly optimized interpolation decimation and filtering units is proposed to adaptively process the observations and suppress jammers and clutter the output is switched to the branch with the best performance according to the minimum variance criterion in order to design the decimation unit we present an optimal decimation scheme and a low complexity decimation scheme we also develop two adaptive implementations for the proposed scheme one based on a recursive least squares rls algorithm and the other on a constrained conjugate gradient ccg algorithm the proposed adaptive algorithms are tested with simulated radar data the simulation results show that the proposed rr sjidf stap schemes with both the rls and the ccg algorithms converge at a very fast speed and provide a considerable sinr improvement over the state of the art reduced rank schemes

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

dichotomies for linear evolutionary equations in banach spaces abstract in this paper we present a characterization for the existence of an exponential dichotomy for a linear evolutionary system on a banach space the theory we present here applies to general time varying linear equations in banach spaces as a result it gives a description of the behavior of the nonlinear dynamics generated by certain nonlinear evolutionary equations in the vicinity of a compact invariant set in the case of dissipative systems our theory applies to the study of the flow in the vicinity of the global attractor the theory formulated here holds for linear evolutionary systems which are uniformly contracting and applies to the study of the linearization of nonlinear equations of the following type a parabolic pdes including systems of reaction diffusion equations and the navier stokes equations b hyperbolic pdes including the nonlinear wave equation and the nonlinear schrodinger equation with dissipation c retarded differential equations and d certain neutral differential delay equations

a roundoff error analysis of the lms adaptive algorithm the steady state output error of the least mean square lms adaptive algorithm due to the finite precision arithmetic of a digital processor is analyzed it is found to consist of three terms 1 the error due to the input data quantization 2 the error due to the rounding of the arithmetic operations in calculating the filter s output and 3 the error due to the deviation of the filter s coefficients from the values they take when infinite precision arithmetic is used the last term is of paricular interest because its mean squared value is inversely proportional to the adaptation step size both fixed and floating point arithmetics are examined and the expressions for the final mean square error are found to be similar the relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

improved estimation in cumulative link models for the estimation of cumulative link models for ordinal data the bias reducing adjusted score equations of firth in 1993 are obtained whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood estimator their form suggests a parameter dependent adjustment of the multinomial counts which in turn suggests the solution of the adjusted score equations through iterated maximum likelihood fits on adjusted counts greatly facilitating implementation like the maximum likelihood estimator the reduced bias estimator is found to respect the invariance properties that make cumulative link models a good choice for the analysis of categorical data its additional finiteness and optimal frequentist properties along with the adequate behaviour of related asymptotic inferential procedures make the reduced bias estimator attractive as a default choice for practical applications furthermore the estimator proposed enjoys certain shrinkage properties that are defensible from an experimental point of view relating to the nature of ordinal data

the dichotomy theorem for evolution bi families we prove that the operator g the closure of the rst order dierential operator d dt d t on l2 r x is fredholm if and only if the not well posed equation u 0 t d t u t t 2 r has exponential dichotomies on r and r and the ranges of the dichotomy projections form a fredholm pair moreover the index of this pair is equal to the fredholm index of g here x is a hilbert space d t a b t a is the generator of a bi semigroup b is a bounded piecewise strongly continuous operator valued function also we prove some perturbations results and consider various examples of not well posed problems

further study on robust adaptive beamforming with optimum diagonal loading significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold these uncertainties may be caused by uncertainty in direction of arrival doa imperfect array calibration near far effect mutual coupling and other mismatch and modeling errors a diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value the major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint in this paper an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed the diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading on demand mechanism rather than fixed continuous or ad hoc loading we additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low snr several numerical simulations with doa mismatch moving jamming and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers

ordinary differential operators in hilbert spaces and fredholm pairs let a t be a path of bounded operators on a real hilbert space hyperbolic at pm infty we study the fredholm theory of the operator f a d dt a t we relate the fredholm property of f a to the stable and unstable linear spaces of the associated system x prime a t x several examples are included to point out the differences with respect to the finite dimensional case in particular concerning the role of the spectral flow we define a general class of paths a for which many properties typical of the finite dimensional framework still hold our motivation is to develop the linear theory which is necessary for the set up of morse homology on hilbert manifolds

the efficiency of multinomial logistic regression compared with multiple group discriminant analysis abstract multinomial logistic regression also referred to as polychotomous logistic regression is frequently used for the analysis of categorical response data with continuous or categorical explanatory variables parameter estimates are usually obtained through direct maximum likelihood estimation normal discriminant analysis has been used as an alternative approach to this methodology although it is strictly appropriate only when the usual normal discriminant assumptions concerning the explanatory variables are valid comparative evaluations of the two procedures including the investigation of bias and efficiency in parameter estimation have been almost entirely limited to the case of two response groups for both normal and nonnormal explanatory variables bull and donner 1987 extended the comparison of logistic regression and normal discrimination in the normal case to more than two response groups deriving the large sample distribution of the slope parameter estimates for each of the two proc

putting background information about relative risks into conjugate prior distributions in bayesian and empirical bayes analyses of epidemiologic data the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector this article describes problems in translating background information about relative risks into conjugate priors and a solution traditionally conjugate priors have been specified through flattening constants an approach that leads to conflicts with the true prior covariance structure for the log relative risks one can however derive a conjugate prior consistent with that structure by using a data augmentation approximation to the true log relative risk prior although a rescaling step is needed to ensure the accuracy of the approximation these points are illustrated with a logistic regression analysis of neonatal death risk

the multiple adaptations of multiple imputation multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large sample public use surveys in the last two decades the multiple imputation framework has been adapted for other statistical contexts for example individual researchers use multiple imputation to handle missing data in small samples statistical agencies disseminate multiply imputed data sets for purposes of protecting data confidentiality and survey methodologists and epidemiologists use multiple imputation to correct for measurement errors in some of these settings rubin s original rules for combining the point and variance estimates from the multiply imputed data sets are not appropriate because what is known and thus the conditional expectations and variances used to derive inferential methods differs from that in the missing data context these applications require new combining rules and methods of inference in fact more than 10 combining rules exist in the published literatur

multiple imputation for interval estimation from simple random samples with ignorable nonresponse abstract several multiple imputation techniques are described for simple random samples with ignorable nonresponse on a scalar outcome variable the methods are compared using both analytic and monte carlo results concerning coverages of the resulting intervals for the population mean using m 2 imputations per missing value gives accurate coverages in common cases and is clearly superior to single imputation m 1 in all cases the performances of the methods for various m can be predicted well by linear interpolation in 1 m 1 between the results for m 2 and m as a rough guide to assure coverages of interval estimates within 2 of the nominal level when using the preferred methods the number of imputations per missing value should increase from 2 to 3 as the nonresponse rate increases from 10 to 60

evans functions jost functions and fredholm determinants the principal results of this paper consist of an intrinsic definition of the evans function in terms of newly introduced generalized matrix valued jost solutions for general first order matrix valued differential equations on the real line and a proof of the fact that the evans function a finite dimensional determinant by construction coincides with a modified fredholm determinant associated with a birman schwinger type integral operator up to an explicitly computable nonvanishing factor

a stochastic conjugate gradient method for the approximation of functions a stochastic conjugate gradient method for the approximation of a function is proposed the proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution in addition the method performs the conjugate gradient steps by using an inner product that is based on stochastic sampling theoretical analysis shows that the method is convergent in probability the method has applications in such fields as predistortion for the linearization of power amplifiers

the index formula and the spectral shift function for relatively trace class perturbations we compute the fredholm index index da of the operator da d dt a on l2 r h associated with the operator path a t t where af t a t f t for a e t r and appropriate f l2 r h via the spectral shift function a a associated with the pair a a of asymptotic operators a a on the separable complex hilbert space h in the case when a t is generally an unbounded relatively trace class perturbation of the unbounded self adjoint operator a we derive a formula an extension of a formula due to pushnitski relating the spectral shift function a a for the pair a a and the corresponding spectral shift function h2 h1 for the pair of operators h2 h1 dada da da in this relative trace class context h2 h1 1 1 2 1 2 a a d 2 1 2for a e 0 this formula is then used to identify the fredholm index of da with 0 a a in addition we prove that index da coincides with the spectral flow spflow a t t of the family a t t r and also relate it to the fredholm perturbation determinant for the pair a a index da spflow a t t 0 a a 1lime 0im ln deth a iei a iei 1 0 h2 h1 with the choice of the branch of ln deth on c such that limim z ln deth a zi a zi 1 0 we also provide some applications in the context of supersymmetric quantum mechanics to zeta function and heat kernel regularized spectral asymmetries and the eta invariant

a novel approach for stabilizing recursive least squares filters a novel approach for stabilizing recursive least squares rls filters is presented the approach relies on a detailed fixed point analysis which provides two important benefits the analysis reveals a bias in the error propagation mechanism providing an analytical basis for instability problems the analysis then indicates which specific roundoff errors are causing instability these roundoff errors are then biased in such a way that the overall filter is biased towards stable performance experimental results indicate that stability can be achieved with negligible loss in least squares performance

alternative paradigms for the analysis of imputed survey data abstract rubin has offered multiple imputation as a general approach to inference from survey data sets with missing values filled in through imputation in many situations the multiple imputation variance estimator is consistent in turn this observation has lent support to a number of complex applications in fact however the multiple imputation variance estimator is inconsistent under some simple conditions this article extends previous work of rao and shao and of fay directed toward consistent variance estimation under wider conditions extensions of rao and shao s results to fractionally weighted imputation combines the estimation efficiency of multiple imputation and the consistency of the rao shao variance estimator

generalized conjugate priors for bayesian analysis of risk and survival regressions le choix pour les analyses bayesiennes portant sur les risques relatifs de distributions a priori conjuguees peut etre tres limitant du fait que la forme de cette distribution depend du parametre de valeur centrale cependant en introduisant separement ce parametre on generalise ces distributions a priori ce qui permet de modeliser une tres large palette d opinions a priori tout en conservant les proprietes de simplicite des calculs propres aux analyses conjuguees cet article illustre les resultats fournis par ces analyses avec des conjuguees generalisees a partir d exemples sur des enquetes cas x temoins dont le but etait d etudier le lien des amenagements en c bles electriques wire codes en zone residentielle et des champs magnetiques avec les cas de leucemie chez l enfant

weighted pseudometric discriminatory power improvement using a bayesian logistic regression model based on a variational method in this paper we investigate the effectiveness of a bayesian logistic regression model to compute the weights of a pseudometric in order to improve its discriminatory capacity and thereby increase image retrieval accuracy in the proposed bayesian model the prior knowledge of the observations is incorporated and the posterior distribution is approximated by a tractable gaussian form using variational transformation and jensen s inequality which allow a fast and straightforward computation of the weights the pseudometric makes use of the compressed and quantized versions of wavelet decomposed feature vectors and in our previous work the weights were adjusted by the classical logistic regression model a comparative evaluation of the bayesian and classical logistic regression models is performed for content based image retrieval as well as for other classification tasks in a decontextualized evaluation framework in this same framework we compare the bayesian logistic regression model to some relevant state of the art classification algorithms experimental results show that the bayesian logistic regression model outperforms these linear classification algorithms and is a significantly better tool than the classical logistic regression model to compute the pseudometric weights and improve retrieval and classification performance finally we perform a comparison with results obtained by other retrieval methods

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

robust reduced rank adaptive algorithm based on parallel subgradient projection and krylov subspace in this paper we propose a novel reduced rank adaptive filtering algorithm exploiting the krylov subspace associated with estimates of certain statistics of input and output signals we point out that when the estimated statistics are erroneous e g due to sudden changes of environments the existing krylov subspace based reduced rank methods compute the point that minimizes a ldquowrongrdquo mean square error mse in the subspace the proposed algorithm exploits the set theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the ldquotruerdquo mse in the subspace therefore compared with the existing methods the proposed algorithm is more suited to adaptive filtering applications a convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method apsm numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

multiple imputation for incomplete data with semicontinuous variables we consider the application of multiple imputation to data containing not only partially missing categorical and continuous variables but also partially missing semicontinuous variables variables that take on a single discrete value with positive probability but are otherwise continuously distributed as an imputation model for data sets of this type we introduce an extension of the standard general location model proposed by olkin and tate our extension the blocked general location model provides a robust and general strategy for handling partially observed semicontinuous variables in particular we incorporate a two level model for the semicontinuous variables into the general location model the first level models the probability that the semicontinuous variable takes on its point mass value and the second level models the distribution of the variable given that it is not at its point mass in addition we introduce em and data augmentation algorithms for the blocked general location model w

krylov proportionate adaptive filtering techniques not limited to sparse systems this paper proposes a novel adaptive filtering scheme named the krylov proportionate normalized least mean square kpnlms algorithm kpnlms exploits the benefits i e fast convergence for sparse unknown systems of the proportionate nlms algorithm but its applications are not limited to sparse unknown systems a set of orthonormal basis vectors is generated from a certain krylov sequence it is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data different adaptation gain is allocated to a coefficient of each basis vector and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate kpnlms enjoys i fast convergence ii linear complexity per iteration and iii no use of any a priori information numerical examples demonstrate significant advantages of the proposed scheme over the reduced rank method based on the multistage wiener filter mwf and the transform domain adaptive filter tdaf both in noisy and silent situations

the morse and maslov indices for multidimensional schrodinger operators with matrix valued potentials we study the schrodinger operator l v on a star shaped domain in rd with lipschitz boundary the operator is equipped with quite general dirichletor robin type boundary conditions induced by operators between h1 2 and h 1 2 and the potential takes values in the set of symmetric n n matrices by shrinking the domain and rescaling the operator we obtain a path in the fredholm lagrangian grassmannian of the subspace of h1 2 h 1 2 corresponding to the given boundary condition the path is formed by computing the dirichlet and neumann traces of weak solutions to the rescaled eigenvalue equation we prove a formula relating the number of negative eigenvalues of l the morse index the signed crossings of the path the maslov index the number of negative eigenvalues of the potential matrix evaluated at the center of the domain and the number of negative eigenvalues of a bilinear form related to the boundary operator

evolutionary semigroups and lyapunov theorems in banach spaces we present a spectral mapping theorem for continuous semigroups of operators on any banach space e the condition for the hyperbolicity of a semigroup on e is given in terms of the generator of an evolutionary semigroup acting in the space of e valued functions the evolutionary semigroup generated by the propagator of a nonautonomous differential equation in e is also studied a discrete technique for investigating the evolutionary semigroup is developed and applied in describing the hyperbolicity exponential dichotomy of the nonautonomous equation

fractional hot deck imputation to compensate for item nonresponse hot deck imputation procedures replace missing values with values that occur in the sample fractional hot deck imputation replaces each missing observation with a set of imputed values and assigns a weight to each imputed value under the model in which observations in an imputation cell are independently and identically distributed fractional hot deck imputation is shown to be an effective imputation procedure a consistent replication variance estimation procedure for estimators computed with fractional imputation is suggested simulations show that fractional imputation and the suggested variance estimator are superior to multiple imputation estimators in general and much superior to multiple imputation for estimating the variance of a domain mean

calculation of polychotomous logistic regression parameters using individualized regressions summary the use of individualized logistic regression in which a series of separate simple logistic regression analyses are performed as a replacement for polychotomous logistic regression is studied the asymptotic relative efficiencies of the individual parameter estimates are observed to be generally high as are the efficiencies of predicted probability estimates and to a somewhat lesser extent joint tests of parameters from different regressions

a warning on the use of chi squared statistics with frequency tables with small expected cell counts abstract when applied to frequency tables with small expected cell counts pearson chi squared test statistics may be asymptotically inconsistent even in cases in which a satisfactory chi squared approximation exists for the distribution under the null hypothesis this problem is particularly important in cases in which the number of cells is large and the expected cell counts are quite variable to illustrate this bias of the chi squared test this article considers the pearson chi squared test of the hypothesis that the cell probabilities for a multinomial frequency table have specified values in this case the expected value and variance of the pearson chi square may be evaluated under both the null and alternative hypotheses when the number of cells is large normal approximations and discrete edgeworth expansions may also be used to assess the size and power of the pearson chi squared test these analyses show that unless all cell probabilities are equal it is possible to select a significance lev