α stable interference modeling and cauchy receiver for an ir uwb ad hoc network in this paper we investigate ad hoc networks based on impulse radio ultra wideband due to multiple access the interference distribution is not gaussian one important reason for errors is the presence of close interferers generating pulse collision however such events are rare and we propose an stable model compatible with this fact due to its heavy tailed distribution we derive the analytical expression of the two significant parameters they depend on the attenuation coefficient the users density the pulse collision probability and the pulse shape we finally propose receiver strategies cauchy receiver and p norm that outperforms the classical gaussian receiver

calibrated propensity score method for survey nonresponse in cluster sampling weighting adjustment is commonly used in survey sampling to correct for unit nonresponse in cluster sampling the missingness indicators are often correlated within clusters and the response mechanism is subject to cluster specific nonignorable missingness based on a parametric working model for the response mechanism that incorporates cluster specific nonignorable missingness we propose a method of weighting adjustment we provide a consistent estimator of the mean or totals in cases where the study variable follows a generalized linear mixed effects model the proposed method is robust in the sense that the consistency of the estimator does not require correct specification of the functional forms of the response and outcome models a consistent variance estimator based on taylor linearization is also proposed numerical results including a simulation and a real data application are presented

a multiplicative ergodic theorem and nonpositively curved spaces we study integrable cocycles u n x over an ergodic measure preserving transformation that take values in a semigroup of nonexpanding maps of a nonpositively curved space y e g a cartan hadamard space or a uniformly convex banach space it is proved that for any y 2 y and almost all x there exist a 0 and a unique geodesic ray t x in y starting at y such that lim n 1 1 n d an x u n x y d 0 in the case where y is the symmetric space gln r on r and the cocycles take values in gln r this is equivalent to the multiplicative ergodic theorem of oseledec two applications are also described the first concerns the determination of poisson boundaries and the second concerns hilbert schmidt operators

spectral correlations of fractional brownian motion fractional brownian motion fbm is a ubiquitous nonstationary model for many physical processes with power law time averaged spectra in this paper we exploit the nonstationarity to derive the full spectral correlation structure of fbm starting from the time varying correlation function we derive two different time frequency spectral correlation functions the ambiguity function and the kirkwood rihaczek spectrum and one dual frequency spectral correlation function the dual frequency spectral correlation has a surprisingly simple structure with spectral support on three discrete lines the theoretical predictions are verified by spectrum estimates of monte carlo simulations and of a time series of earthquakes with a magnitude of 7 and higher

on inconsistent bayes estimates of location on montre que dans certaines situations relativement naturelles les estimateurs de position bayesiens sont inconsistants

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

a class of non gaussian processes for monte carlo simulation a new model is proposed to represent non gaussian stationary processes and develop monte carlo simulation algorithms for generating sample paths of non gaussian processes the model is based on a class of non gaussian processes the class of conditional gaussian processes two representations are considered for these processes the first representation is based on a randomized version of the classical spectral density function the second representation uses the output of a linear filter with random coefficients subjected to gaussian noise to define conditional gaussian processes the proposed model its representations and corresponding monte carlo simulation algorithms are illustrated by examples involving non gaussian random variables and processes it is shown that the proposed model can match any second moment properties but generally can only fit approximately a specified marginal distribution

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

performance analysis of ldpc coded diversity combining on rayleigh fading channels with impulsive noise spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with low density parity check ldpc codes it can achieve excellent error correcting performance noise added at each branch of the diversity combiner is generally assumed to be additive white gaussian noise but there are many applications where the received signal is impaired by noise with a non gaussian distribution in this paper we derive the exact bit error probability of different linear combining techniques on rayleigh fading channels with impulsive noise which is modeled using symmetric alpha stable distributions the relationship for the signal to noise ratios of these linear combiners is derived and then different non linear detectors are presented a detector based on the bi parameter cauchy gaussian mixture model is used and shows near optimal performance with a significant reduction in complexity when compared with the optimal detector furthermore the threshold signal to noise ratio of ldpc codes for different combining techniques on these channels is derived using density evolution and an estimation of the waterfall performance of ldpc codes is derived that reduces the gap between simulated and asymptotic performance

random walks at random times convergence to iterated levy motion fractional stable motions and other self similar processes for a random walk defined for a doubly infinite sequence of times we let the time parameter itself be an integer valued process and call the orginal process a random walk at random time we find the scaling limit which generalizes the so called iterated brownian motion khoshnevisan and lewis ann appl probab 9 1999 629 667 suggested the existence of a form of measure theoretic duality between iterated brownian motion and a brownian motion in random scenery we show that a random walk at random time can be considered a random walk in alternating scenery thus hinting at a mechanism behind this duality following cohen and samorodnitsky ann appl probab 16 2006 1432 1461 we also consider alternating random reward schema associated to random walks at random times whereas random reward schema scale to local time fractional stable motions we show that the alternating random reward schema scale to indicator fractional stable motions finally we show that one may recursively subordinate random time processes to get new local time and indicator fractional stable motions and new stable processes in random scenery or at random times when 2 the fractional stable motions given by the recursion are fractional brownian motions with dyadic h 0 1 also we see that un subordinating via a time change allows one to in some sense extract brownian motion from fractional brownian motions with h 1 2

particle tracking for fractional diffusion with two time scales abstract previous work y zhang m m meerschaert b baeumer particle tracking for time fractional diffusion phys rev e 78 2008 036705 showed how to solve time fractional diffusion equations by particle tracking this paper extends the method to the case where the order of the fractional time derivative is greater than one a subordination approach treats the fractional time derivative as a random time change of the corresponding cauchy problem with a first derivative in time one novel feature of the time fractional case of order greater than one is the appearance of clustering in the operational time subordinator which is non markovian solutions to the time fractional equation are probability densities of the underlying stochastic process the process models movement of individual particles the evolution of an individual particle in both space and time is captured in a pair of stochastic differential equations or langevin equations monte carlo simulation yields particle location and the ensemble density approximates the solution to the variable coefficient time fractional diffusion equation in one or several spatial dimensions the particle tracking code is validated against inverse transform solutions in the simplest cases further applications solve model equations for fracture flow and upscaling flow in complex heterogeneous porous media these variable coefficient time fractional partial differential equations in several dimensions are not amenable to solution by any alternative method so that the grid free particle tracking approach presented here is uniquely appropriate

heavy tailed log hydraulic conductivity distributions imply heavy tailed log velocity distributions 1 equations of contaminant transport describing non gaussian dispersion of solute in heterogeneous porous media have been developed by several authors e g berkowitz and scher 1995 1998 benson 1998 2001 berkowitz et al 2000 and baeumer et al 2005 the equations assume that solute particle movement in time and or space can be described by heavy tailed probability distributions e g levy stable distributions this assumption requires a mechanism for solute particles to move through heterogeneous porous media in a manner that can be approximated with heavy tailed probability distributions this work investigates whether a heavy tailed levy stable distribution of increments in log hydraulic conductivity results in a heavy tailed distribution of increments in log velocity a heavy tailed distribution of increments in log velocity would be a mechanism for solute particle movement in time or space that can be described by a heavy tailed probability distribution a computer algorithm was written to generate realistic hydraulic conductivity fields the algorithm modifies the spectral synthesis method for generating fractional brownian motion i e saupe 1988 and brewer and wheatcraft 1994 and produces self similar hydraulic conductivity fields with a heavy tailed levy stable distribution of increments in log hydraulic conductivity a monte carlo approach was adopted in which 100 hydraulic conductivity fields were generated for each of the following values of 0 8 1 1 1 4 and 1 7 the usgs finite difference groundwater code modflow was used to calculate the velocity fields and the increments in longitudinal log hydraulic conductivity and log velocity from the fields were analyzed to determine whether they were consistent with a heavy tailed levy stable probability density function pdf after determining that the distributions of increments in log hydraulic conductivity and log velocity were consistent with a levy stable pdf the tail parameters describing each pair of hydraulic conductivity and velocity fields were estimated with the nolan 1997 maximum likelihood estimator the relationship between the two tail parameters was then determined there are three conclusions of this research first mandelbrot and pp plots confirm that levy stable distributions of increments in log hydraulic conductivity give rise to levy stable distributions of increments in log velocity second the tail parameter for the increments in log velocity is typically smaller indicating a heavier probability tail than the corresponding tail parameter for the increments in log hydraulic conductivity third there is a positive statistical relation between the two tail parameters

brief paper stochastic tube mpc with state estimation an output feedback model predictive control mpc strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed given the probability distributions of the disturbance input the measurement noise and the initial state estimation error the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator from these distributions a set of deterministic constraints is computed for the predictions of a nominal model the constraints are incorporated in a receding horizon optimization of an expected quadratic cost which is formulated as a quadratic program the constraints are constructed so as to provide a guarantee of recursive feasibility and the closed loop system is stable in a mean square sense all uncertainties in this paper are taken to be bounded in most control applications this gives a more realistic representation of process and measurement noise than the more traditional gaussian assumption

simple random walk on long range percolation clusters ii scaling limits supported in part at the technion by a landau fellowship supported in part by an alfred sloan fellowship in mathematics

harmonic oscillator under levy noise unexpected properties in the phase space a harmonic oscillator under the influence of noise is a basic model of various physical phenomena under gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate gaussian distribution with elliptic level lines the distribution of phase is homogeneous none of these properties hold in the general levy case thus the level lines of the joint probability density are not elliptic the coordinate and the velocity of the oscillator are strongly dependent and this dependence is quantified by introducing the corresponding parameter width deficit the distribution of the phase is inhomogeneous and highly nontrivial

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

a subspace based direction finding algorithm using fractional lower order statistics we propose several classes of fractional lower order moment flom based matrices that can be used with music to estimate the doas of independent circular signals embedded in additive s spl alpha s symmetric spl alpha stable noise e g sea clutter we run simulations with different choices of the flom parameter p for our flom based matrices and conclude that when the noise is s spl alpha s with unknown spl alpha spl ne 2 flom multiple signal classification music with p close to unity yields good performance the performance of flom music and robust covariation based roc music are similar three scenarios that contain circular signals phase modulation pm circularly symmetrical gaussian and quaternary phase shift keying qpsk and one scenario that contains noncircular signals binary phase shift keying bpsk all embedded in the same s spl alpha s noise are tested these simulation results reveal that the scenario containing bpsk signals leads to poor performance indicating that flom music is presently limited to circular signals

nonlinear system identification in impulsive environments nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics in many practical applications impulsive measurement noise severely weakens the effectiveness of conventional methods in this paper spl alpha stable noise is used as a noise model in such case the minimum mean square error mmse criterion is no longer an appropriate metric for estimation error due to the lack of finite second order statistics of the noise therefore we adopt minimum dispersion criterion which in turn leads to the adaptive least mean pth power lmp algorithm it is shown that the lmp algorithm under the spl alpha stable noise model converges as long as the step size satisfies certain conditions the effect of p on the performance is also investigated compared with conventional methods the proposed method is more robust to impulsive noise and has better performance

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

a bayesian discovery procedure we discuss a bayesian discovery procedure for multiple comparison problems we show that under a coherent decision theoretic framework a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative under a semi parametric model for the data we show that the bayes rule can be approximated by the optimal discovery procedure odp recently introduced by storey 2007a improving the approximation leads us to a bayesian discovery procedure bdp which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model we compare the bdp and the odp estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples we extend the setting of the odp by discussing modifications of the loss function that lead to different single thresholding statistics finally we provide an application of the previous arguments to dependent spatial data

merging multiple longitudinal studies with study specific missing covariates a joint estimating function approach merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power this article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics such as different follow up schedules and study specific missing covariates e g covariates observed in some studies but missing in other studies the presence of study specific missing covariates presents great statistical methodology challenge in data merging and analysis we propose a joint estimating function approach to addressing this challenge in which a novel nonparametric estimating function constructed via splines based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates under mild regularity conditions we show that the proposed estimator is consistent and asymptotically normal we evaluate finite sample performances of the proposed method through simulation studies in comparison to the conventional multiple imputation approach our method exhibits smaller estimation bias we provide an illustrative data analysis using longitudinal cohorts collected in mexico city to assess the effect of lead exposures on children s somatic growth

ornstein uhlenbeck process with fluctuating damping abstract this paper studies langevin equation with random damping due to multiplicative noise and its solution two types of multiplicative noise namely the dichotomous noise and fractional gaussian noise are considered their solutions are obtained explicitly with the expressions of the mean and covariance determined explicitly properties of the mean and covariance of the ornstein uhlenbeck process with random damping in particular the asymptotic behavior are studied the effect of the multiplicative noise on the stability property of the resulting processes is investigated

the gradually truncated levy flight for systems with power law distributions abstract power law distributions have been observed in various economical and physical systems levy flights have infinite variance which discourage a physical approach we introduce a class of stochastic processes the gradually truncated levy flight in which large steps of a levy flight are gradually eliminated it has finite variance and the system can be analyzed in a closed form we applied the present method to explain the distribution of a particular economical index the present method can be applied to describe time series in a variety of fields i e turbulent flow anomalous diffusion polymers etc

expected estimating equations to accommodate covariate measurement error estimating equations which are not necessarily likelihood based score equations are becoming increasingly popular for estimating regression model parameters this paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects but surrogate or mismeasured covariates are available instead the method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data we propose to base estimation on the expectation of the complete data estimating equation conditioned on available data the regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations the expected estimating equation eee estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data a pseudo eee estimator which requires less computation is also investigated asymptotic distribution theory is derived small sample simulations are conducted when the error process is an order 1 autoregressive model regression calibration is extended to this setting and compared with the eee approach we demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity

partly conditional estimation of the effect of a time dependent factor in the presence of dependent censoring we propose semiparametric methods for estimating the effect of a time dependent covariate on treatment free survival the data structure of interest consists of a longitudinal sequence of measurements and a potentially censored survival time the factor of interest is time dependent treatment free survival is of interest and is dependently censored by the receipt of treatment patients may be removed from consideration for treatment temporarily or permanently the proposed methods combine landmark analysis and partly conditional hazard regression a set of calendar time cross sections is specified and survival time from cross section date is modeled through weighted cox regression the assumed model for death is marginal in the sense that time varying covariates are taken as fixed at each landmark with the mortality hazard function implicitly averaging across future covariate trajectories dependent censoring is overcome by a variant of inverse probability of censoring weighting ipcw the proposed estimators are shown to be consistent and asymptotically normal with consistent covariance estimators provided simulation studies reveal that the proposed estimation procedures are appropriate for practical use we apply the proposed methods to pre transplant mortality among end stage liver disease esld patients

wavelet based parameter estimation for polynomial contaminated fractionally differenced processes we consider the problem of estimating the parameters for a stochastic process using a time series containing a trend component trend i e large scale variations in the series that are best modeled outside of a stochastic framework is often confounded with low frequency stochastic fluctuations this problem is particularly evident in models such as fractionally differenced fd processes which exhibit slowly decaying autocorrelations and can be extended to encompass nonstationary processes with substantial low frequency components we use the discrete wavelet transform dwt to estimate parameters for stationary and nonstationary fd processes in a model of polynomial trend plus fd noise using daubechies wavelet filters allows for automatic elimination of polynomial trends due to embedded differencing operations parameter estimation is based on an approximate maximum likelihood approach made possible by the fact that the dwt decorrelates fd processes approximately we consider this decorrelation in detail examining the between and within scale wavelet correlations separately better between scale decorrelation can be achieved by increasing the length of the wavelet filter whereas the within scale correlations can be handled via explicit modeling by a low order autoregressive process we demonstrate our methodology by applying it to a popular climate dataset

on the value distribution of the epstein zeta function in the critical strip we study the value distribution of the epstein zeta function e n l s for 0 infinity we prove that the random variable v n 2c e n cn has a limit distribution which we give explicitly here v n is the volume of the n dimensional unit ball more generally for any fixed epsilon 0 we determine the limit distribution of the random function c bar right arrow v n 2c e n cn c epsilon 1 4 epsilon 1 2 epsilon after compensating for the pole at c 1 2 we even obtain a limit result on the whole interval 1 4 epsilon 1 2 and as a special case we deduce the following strengthening of a result by sarnak and strombergsson concerning the height function h n l of the flat torus r n l the random variable n h n l log 4 pi gamma 1 log n has a limit distribution as n infinity which we give explicitly finally we discuss a question posed by sarnak and strombergsson as to whether there exists a lattice l subset of r n for which e n l s has no zeros in 0 infinity

superdiffusive limits for deterministic fast slow dynamical systems we consider deterministic fast slow dynamical systems on mathbb r m times y of the form begin aligned left begin array ll x k 1 n x k n n 1 a big x k n big n 1 alpha b big x k n big v y k y k 1 f y k end array right end aligned where alpha in 1 2 under certain assumptions we prove convergence of the m dimensional process x n t x lfloor nt rfloor n to the solution of the stochastic differential equation begin aligned mathrm d x a x mathrm d t b x diamond mathrm d l alpha end aligned where l alpha is an alpha stable levy process and diamond indicates that the stochastic integral is in the marcus sense in addition we show that our assumptions are satisfied for intermittent maps f of pomeau manneville type

stability and lack of memory of the returns of the hang seng index abstract in this paper we show that the logarithmic returns of the hang seng index from january 2 1987 to november 14 2005 statistically resemble a sequence of independent identically distributed levy stable random variables this is in stark contrast to xiu and jin 2007 39 where long memory farima processes with gaussian noise were suggested as well fitted to the data the lack of memory is checked by using lo s modified r s statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean squared displacement in order to test stability of the data we employ several statistical tests based on the empirical distribution function finally we also show that the returns possess no conditional heteroscedasticity property thus excluding the arch garch family of processes as possible underlying models

the method of simulated quantiles we introduce an inference method based on quantiles matching which is useful for situations where the density function does not have a closed form but it is simple to simulate and or moments do not exist functions of theoretical quantiles which depend on the parameters of the assumed probability law are matched with sample quantiles which depend on observations since the theoretical quantiles may not be available analytically the optimization is based on simulations we illustrate the method with the estimation of stable distributions a thorough monte carlo study and an illustration to 22 nancial indexes show

parametric fractional imputation for missing data analysis under a parametric model for missing data the em algorithm is a popular tool for flnding the maximum likelihood estimates mle of the parameters of the model imputation when carefully done can be used to facilitate the parameter estimation by applying the complete sample estimators to the imputed dataset the basic idea is to generate the imputed values from the conditional distribution of the missing data given the observed data multiple imputation is a bayesian approach to generate the imputed values from the conditional distribution in this article parametric fractional imputation is proposed as a parametric approach for generating imputed values using fractional weights the e step of the em algorithm can be approximated by the weighted mean of the imputed data likelihood where the fractional weights are computed from the current value of the parameter estimates some computational e ciency can be achieved using the idea of importance sampling in the monte carlo approximation of the conditional expectation the resulting estimator of the specifled parameters will be identical to the mle under missing data if the fractional weights are adjusted using a calibration step the proposed imputation method provides e cient parameter estimates for the model parameters specifled and also provides reasonable estimates for parameters that are not part of the imputation model for example domain means thus the proposed imputation method is a useful tool for general purpose data analysis variance estimation is covered and results from a limited simulation study are presented

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

an rkhs formulation of the inverse regression dimension reduction problem suppose that y is a scalar and x is a second order stochastic process where y and x are conditionally independent given the random variables 1 p which belong to the closed span l2 of x this paper investigates a unified framework for the inverse regression dimension reduction problem it is found that the identification of l2 with the reproducing kernel hilbert space of x provides a platform for a seamless extension from the finite to infinite dimensional settings it also facilitates convenient computational algorithms that can be applied to a variety of models

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

within cluster resampling for multilevel models under informative cluster size a within cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster we then estimate the parameters by maximising an average over the bootstrap samples of a suitable composite log likelihood the consistency of the proposed estimator is shown 15 and does not require that the correct model for cluster size is specified we give an estimator of the covariance matrix of the proposed estimator and a test for the non informativeness of the cluster sizes a simulation study shows as in neuhaus mcculloch 2011 that the standard maximum likelihood estimator exhibits little bias for some regression coefficients however for those parameters which exhibit non negligible bias the proposed method is successful in cor 20 recting for this bias

memoryless discrete time signal detection in long range dependent noise the problem of designing optimum memoryless detectors for known signals in long range dependent lrd noise is considered in particular under the performance criterion of asymptotic relative efficiency are optimum memoryless detection in lrd noise is investigated by exploiting the hermite expansions the detectors considered have the form of a nonlinearity followed by an accumulator and threshold comparator it is shown that when the noise is lrd and gaussian all nonlinearities with hermite rank one are asymptotically equivalent in terms of efficiency and are most powerful moreover the optimum nonlinearities with hermite rank greater than one are given by the corresponding hermite polynomials the case of non gaussian lrd noise that can be derived by nonlinear transformation of gaussian noise is also considered in this case the globally optimum nonlinearity is very difficult to obtain in general instead we proposed a suboptimal nonlinearity which is given by a linear combination of the corresponding locally optimum detector and the inverse of the transform function generating the noise simulations show that the proposed detector outperforms the locally optimal detector for lrd non gaussian noise

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

tempered stable levy motion driven by stable subordinator a b s t r a c t in this article we propose a new model for financial data description combining two independent mechanisms namely the tempered stable process and inverse stable subordinator we obtain a new model which captures not only the tempered stable character of the underlying data but also such a property as periods in which the values of an asset stay on the same level moreover we classify our system to the family of subdiffusive processes and investigate its tail behavior we describe in detail testing and estimation procedures for the proposed model in the last step we calibrate our model to the real data

a unified approach to linearization variance estimation from survey data after imputation for item nonresponse variance estimation after imputation is an important practical problem in survey sampling when deterministic imputation or stochastic imputation is used we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach we provide some applications of the approach to regression imputation fractional categorical imputation multiple imputation and composite imputation results from a simulation study under a factorial structure for the sampling response and imputation mechanisms show that the proposed linearization variance estimator performs well in terms of relative bias assuming a missing at random response mechanism

erratum to a stochastic controller for a scalar linear system with additive cauchy noise automatica 50 1 2014 114 127 abstract a stochastic control scheme is developed for scalar discrete time and linear dynamic systems driven by cauchy distributed process and measurement noises when addressing the optimal control problem for such systems the standard quadratic cost criteria cannot be used in this study we introduce a new objective function that is functionally similar to the cauchy probability density function the performance index defined as the expectation of this objective function with respect to the cauchy densities exists the dynamic programming solution to the fixed and finite horizon optimal control problem that uses this performance index appears to be intractable therefore a moving horizon optimal model predictive control problem is implemented for which the conditional expected value of the objective function and its gradients can be computed in closed form and without assumptions such as certainty equivalence numerical results are shown for this m step model predictive optimal controller and compared to a similar linear exponential gaussian model predictive controller an essential difference between the cauchy and gaussian controllers when applied to a system with cauchy noises is that while the gaussian controller is linear and reacts strongly to all noise pulses the cauchy controller can differentiate between measurement and process noise pulses by ignoring the former while responding to the latter this property of the cauchy controller occurs when an impulsive measurement noise is more likely than an impulsive process noise the cauchy and gaussian controllers react similarly when applied to a system with gaussian noises demonstrating the robustness of the proposed control scheme

consistency of bayes estimators of a binary regression function when do nonparametric bayesian procedures overfit to shed light on this question we consider a binary regression problem in detail and establish frequentist consistency for a certain class of bayes procedures based on hierarchical priors called uniform mixture priors these are defined as follows let v be any probability distribution on the nonnegative integers to sample a function f from the prior v first sample m from v and then sample f uniformly from the set of step functions from 0 1 into 0 1 that have exactly m jumps i e sample all m jump locations and m 1 function values independently and uniformly the main result states that if a data stream is generated according to any fixed measurable binary regression function f o 1 2 then frequentist consistency obtains that is for any v with infinite support the posterior of v concentrates on any l1 neighborhood of f 0 solution of an associated large deviations problem is central to the consistency proof

zero order statistics a mathematical framework for the processing and characterization of very impulsive signals impulsive or heavy tailed processes with infinite variance appear naturally in a variety of practical problems that include wireless communications teletraffic hydrology geology and economics most signal processing and statistical methods available in the literature have been designed under the assumption that the processes possess finite variance and they usually break down in the presence of infinite variance although methods based on fractional lower order statistics flos have proven successful in dealing with infinite variance processes they fail in general when the noise distribution has very heavy algebraic tails in this paper we introduce a new approach to statistical moment characterization which is well defined over all processes with algebraic or lighter tails unlike flos these zero order statistics zos as we will call them provide a common ground for the analysis of basically any distribution of practical use known today three new parameters namely the geometric power the zero order location and the zero order dispersion constitute the foundation of zos they play roles similar to those played by the power the expected value and the standard deviation in the theory of second order processes we analyze the properties of the new parameters and derive a zos framework for location estimation that gives rise to a novel mode type estimator with important optimality properties under very impulsive noise several simulations are presented to illustrate the potential of zos methods

the stochastic geometry analyses of cellular networks with alpha stable self similarity to understand the spatial deployment of base stations bss is the first step to analyze the performance of cellular networks and further design efficient networking protocols poisson point process ppp which has been widely adopted to characterize the deployment of bss and established the reputation to give tractable results in the stochastic geometry analyses usually assumes a static bs deployment density in homogeneous ppp hppp models or delicately designed location dependent density functions in in homogeneous ppp models however the simultaneous existence of attractiveness and repulsiveness among bss practically deployed in a large scale area defies such an assumption and the alpha stable distribution one kind of heavy tailed distributions has recently demonstrated superior accuracy to statistically model the varying bs density in different areas in this paper we start with these new findings and investigate the intrinsic feature i e the spatial self similarity embedded in the bss afterwards we refer to a generalized ppp setup with alpha stable distributed density and theoretically derive the related coverage probability in particular we give an upper bound of the derived coverage probability for high signal to interference plus noise ratio thresholds and show the monotonically decreasing property of this bound with respect to the variance of bs density besides we prove that our model could reduce to the single tier hppp for some special cases and demonstrate the superior accuracy of the alpha stable model to approach the real environment

on stochastic differential equations driven by a cauchy process and other stable levy motions we consider the class of one dimensional stochastic differential equations dx t b x t dz t t 0 where b is a borel measurable real function and z is a strictly stable levy process 0 2 weak solutions are investigated improving previous results of the author in various ways in particular for the equation driven by a strictly 1 stable levy process a sufficient existence condition is proven also we extend the weak existence and uniqueness exact criteria due to engelbert and schmidt for the brownian case i e a 2 to the class of equations with a such that 1 2 the results employ some representation properties with respect to strictly stable levy processes

a multivariate distribution for sub images a new method for obtaining multivariate distributions for sub images of natural images is described the information in each sub image is summarized by a measurement vector in a measurement space the dimension of the measurement space is reduced by applying a random projection to the truncated output of the discrete cosine transforms of the sub images the measurement space is then reparametrized such that a gaussian distribution is a good model for the measurement vectors in the reparametrized space an ornstein uhlenbeck process associated with the gaussian distribution is used to model the differences between measurement vectors obtained from matching sub images the probability of a false alarm and the probability of accepting a correct match are calculated the accuracy of the resulting statistical model for matching sub images is tested using images from the middlebury stereo database with promising results in particular if the probability of accepting a correct match is relatively large then there is good agreement between the calculated and the experimental probabilities of obtaining a unique match that is also a correct match

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

stochastic sub additivity approach to the conditional large deviation principle given two polish spaces a x and ay let p a x x a y r d be a bounded measurable function let x x n n 1 and y y n n 1 be two independent stationary processes on a x and a y respectively the article studies the large deviation principle ldp for n 1 n k 1 x k y k conditional on x based on a stochastic version of approximate sub additivity it is shown that if y satisfies certain mixing condition then for almost all random realization x of x the laws of n 1 n k 1 x k y k satisfy the conditional ldp with a non random convex rate function conditions for the rate function to be non trivial that is not 0 function are also given

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

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

nonparametric reconstruction of a multifractal function from noisy data we estimate a real valued function f of d variables subject to additive gaussian perturbation at noise level varepsilon 0 under l loss for 1 the main novelty is that f can have an extremely varying local smoothness exhibiting a so called multifractal behaviour the results of jaffard on the frisch parisi conjecture suggest to link the singularity spectrum of f to besov properties of the signal that can be handled by wavelet thresholding for denoising purposes we prove that the optimal minimax rate of estimation of multifractal functions with singularity spectrum d h has explicit representation varepsilon 2v d bullet pi with v d bullet pi min h frac h left d d h right pi 2h d the minimum is taken over a specific domain and the rate is corrected by logarithmic factors in some cases in particular the usual rate varepsilon 2s 2s d is retrieved for monofractal functions with spectrum reduced to a single value s irrespectively of more interestingly the sparse case of estimation over single besov balls has a new interpretation in terms of multifractal analysis

importance sampling via the estimated sampler monte carlo importance sampling for evaluating numerical integration is discussed we consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood the proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution the argument is closely related to the discussion of the paradox in henmi eguchi 2004 we focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance

on the scaling of the distribution of daily price fluctuations in the mexican financial market index abstract in this paper a statistical analysis of log return fluctuations of the ipc the mexican stock market index is presented a sample of daily data covering the period from 04 09 2000 04 09 2010 was analyzed and fitted to different distributions tests of the goodness of fit were performed in order to quantitatively asses the quality of the estimation special attention was paid to the impact of the size of the sample on the estimated decay of the distributions tail in this study a forceful rejection of normality was obtained on the other hand the null hypothesis that the log fluctuations are fitted to a stable levy distribution cannot be rejected at the 5 significance level

on inconsistent bayes estimates in the discrete case consider sampling from an unknown probability distribution on the integers with a tail free prior the posterior distribution is consistent with a mixture of a tail free prior and a point mass however the posterior may be inconsistent this is likewise true for a countable mixture of tail free priors similar results are given for dirichlet priors

the consistency of posterior distributions in nonparametric problems we give conditions that guarantee that the posterior probability of every hellinger neighborhood of the true distribution tends to 1 almost surely the conditions are 1 a requirement that the prior not put high mass near distributions with very rough densities and 2 a requirement that the prior put positive mass in kullback leibler neighborhoods of the true distribution the results are based on the idea of approximating the set of distributions with a finite dimensional set of distributions with sufficiently small hellinger bracketing metric entropy we apply the results to some examples

on the stationary distribution of iterative imputations iterative imputation in which variables are imputed one at a time each given a model predicting from all the others is a popular technique that can be convenient and exible as it replaces a potentially dicult multivariate modeling problem with relatively simple univariate regressions in this paper we begin to characterize the stationary distributions of iterative imputations and their statistical properties more precisely when the conditional models are compatible dened in the text we give a set of sucient conditions under which the imputation distribution converges in total variation to the posterior distribution of a bayesian model when the conditional models are incompatible but are valid we show that the combined imputation estimator is consistent

new approaches to bayesian consistency we use martingales to study bayesian consistency we derive sufficient conditions for both hellinger and kullback leibler consistency which do not rely on the use of a sieve alternative sufficient conditions for hellinger consistency are also found and demonstrated on examples

inference using surrogate outcome data and a validation sample summary in the context of estimating 3 from the regression model p yi x relating response y to covariates x suppose that only a surrogate response s is available for most study subjects suppose that for a random subsample of the study cohort termed the validation sample the true outcome y is available in addition to s we consider maximum likelihood estimation of 3 from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome p s i y x an alternative semiparametric method is also considered which is nonparametric with respect to p s i y x large sample distribution theory for maximum estimated likelihood estimates is developed an illustrative example is presented

monte carlo likelihood inference for missing data models we describe a monte carlo method to approximate the maximum likelihood estimate mle when there are missing data and the observed data likelihood is not available in closed form this method uses simulated missing data that are independent and identically distributed and independent of the observed data our monte carlo approximation to the mle is a consistent and asymptotically normal estimate of the minimizer of the kullback leibler information as both monte carlo and observed data sample sizes go to infinity simultaneously plug in estimates of the asymptotic variance are provided for constructing confidence regions for we give logit normal generalized linear mixed model examples calculated using an r package

characteristic functions of random variables attracted to 1 stable laws the domain of attraction of a 1 stable law on r d is characterized by the expansions of the characteristic functions of its elements

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

moment analysis for spatiotemporal fractional dispersion 1 the evolution of the first five nonnegative integer order spatial moments corresponding to the mass mean variance skewness and kurtosis are investigated systematically for spatiotemporal nonlocal fractional dispersion three commonly used fractional order transport equations including the time fractional advection dispersion equation time fade the fractal mobile immobile mim equation and the fully fractional advection dispersion equation ffade are considered analytical solutions verify our numerical results and reveal the anomalous evolution of the moments following adams and gelhar s 1992 work on the classical ade we find that a simultaneous analysis of all moments is critical in discriminating between different nonlocal models the evolution of dispersion among the subdiffusive to superdiffusive rates is then further explored numerically by a non markovian random walk particle tracking method that can be used for any heterogeneous boundary or initial value problem in three dimensions both the analytical and the numerical results also show the similarity at the early time and the difference at the late time of moment growth for solutes in different phases mobile versus total described by the mim models further simulations of the 1 d bromide snapshots measured at the made experiments using all three models with parameters fitted by the observed zeroth to fourth moments indicate that 1 both the time and space nonlocality strongly affect the solute transport at the made site 2 all five spatial moments should be considered in transport model selection and calibration because those up to the variance cannot effectively discriminate between nonlocal models and 3 the log concentration should be used when evaluating the plume leading edge and the effects of space nonlocality

convergence rates of posterior distributions we consider the asymptotic behavior of posterior distributions and bayes estimators for infinite dimensional statistical models we give general results on the rate of convergence of the posterior measure these are applied to several examples including priors on finite sieves log spline models dirichlet processes and interval censoring

option pricing beyond black scholes based on double fractional diffusion abstract we show how the prices of options can be determined with the help of double fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the black scholes formula

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

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

rates of convergence of posterior distributions we compute the rate at which the posterior distribution concentrates around the true parameter value the spaces we work in are quite general and include infinite dimensional cases the rates are driven by two quantities the size of the space as measured by bracketing entropy and the degree to which the prior concentrates in a small ball around the true parameter we consider two examples

analysis of longitudinal binary data from multiphase sampling the efficient use of surrogate or auxiliary information has been investigated within both model based and design based approaches to data analysis particularly in the context of missing data here we consider the use of such data in epidemiological studies of disease incidence in which surrogate measures of disease status are available for all subjects at two time points but definitive diagnoses are available only in stratified subsamples we briefly review methods for the analysis of two phase studies of disease prevalence at a single time point and we discuss the extension of four of these methods to the analysis of incidence studies their performance is compared with special reference to a study of the incidence of senile dementia