nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

further asymptotic upper bounds on the minimum distance of trellis codes asymptotic upper bounds on the minimum distance of trellis codes are derived a universal bound and bounds specific to phase shift keying psk and quadrature amplitude modulation qam signal sets are obtained

tail ordering and asymptotic efficiency of rank tests on considere une relation d ordre partiel qui est entre la relation d ordre stochastique definie par lehmann 1955 et une relation d ordre associee a la propriete du rapport de vraisemblance monotone

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

hierarchical models a current computational perspective 2000 hierarchical models a current computational perspective journal of the american statistical association vol 95 no 452 pp 1312 1316

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

on the effectiveness of monte carlo for initial uncertainty forecasting in nonlinear dynamical systems abstract this paper considers the problem of initial uncertainty forecasting in deterministic nonlinear continuous time dynamical systems via particle ensembles the popular monte carlo method which while simple to implement faces fundamental issues in particular it is not clear how well the propagated particles continue to represent the true state uncertainty at future times this paper evaluates the performance of monte carlo forecasting by analyzing it in the context of markov chain monte carlo mcmc theory the propagated ensemble is viewed as the realization of a markov chain at each time instant generated by an associated instantaneous transition kernel it is shown that for a special class of nonlinear systems that have zero divergence the propagated kernel is in detailed balance with the true state probability density function this guarantees statistical consistency of the monte carlo ensemble with the truth at all times for such systems on the other hand no such guarantee is possible for systems with non zero divergence

geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms we develop results on geometric ergodicity of markov chains and apply these and other recent results in markov chain theory to multidimensional hastings and metropolis algorithms for those based on random walk candidate distributions we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution by phrasing the conditions in terms of the curvature of the densities we show that the results apply to all distributions with positive densities in a large class which encompasses many commonly used statistical forms from these results we develop central limit theorems for the metropolis algorithm converse results showing non geometric convergence rates for chains where the rejection rate is not bounded away from unity are also given these show that the negative definiteness property is not redundant

estimation of survival functions under uniform stochastic ordering abstract if s and t are survival functions for two life distributions then s is said to be uniformly stochastically smaller than t denoted by s t if x s x t x is nonincreasing in x on x t x 0 this ordering is transitive uniform stochastic ordering uso has found important applications in nonparametric accelerated life testing among other areas it has been shown that the nonparametric maximum likelihood estimator npmle of s under uso when t is known is inconsistent dykstra kochar robertson derived the restricted npmle s of several unknown survival functions linearly ordered by uso this article shows that these too are inconsistent in general rojo and samaniego gave excellent ad hoc estimators of s and t when the other is known based on their idea for the one sample problem they gave two ad hoc estimators one of them only implied of s and t when they are both unknown these are consistent but they lack some desirable properties this article introduces a one parameter famil

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on the convergence of monte carlo maximum likelihood calculations summary monte carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models given any family he 0 e 0 of non negative integrable functions maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by monte carlo simulation the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0 x remain continuous then with probability 1 the monte carlo approximant to the log likelihood hypoconverges to the exact log likelihood its maximizer converges to the exact maximum likelihood estimate approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood support regions converge to the exact sets in painleve kuratowski set convergence the same results hold when there are missing data if a wald type integrability condition is satisfied asymptotic normality of the monte carlo error and convergence of the monte carlo approximation to the observed fisher information are also shown

on the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint we identify the asymptotic behavior of the estimators proposed by rojo and samaniego and mukerjee of a distribution f assumed to be uniformly stochastically smaller than a known baseline distribution g we show that these estimators are sqrt n convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function by examining the mean squared error of the limit distribution we are able to identify the optimal estimator within mukerjee s class under a variety of different assumptions on f and g similar theoretical results are developed for the two sample problem where f and g are both unknown the asymptotic distribution theory is applied to obtain confidence bands for the survival function bar f based on published data from an accelerated life testing experiment

consistent estimation of distributions with type ii bias with applications in competing risks problems a random variable x is symmetric about 0 if x and x have the same distribution there is a large literature on the estimation of a distribution function df under the symmetry restriction and tests for checking this symmetry assumption often the alternative describes some notion of skewness or one sided bias various notions can be described by an ordering of the distributions of x and x one such important ordering is that p 0 0 the distribution of x is said to have a type ii positive bias in this case if x has a density f then this corresponds to the density ordering f x f x for x 0 it is known that the nonparametric maximum likelihood estimator npmle of the df under this restriction is inconsistent we provide a projection type estimator that is similar to a consistent estimator of two dfs under uniform stochastic ordering where the npmle also fails to be consistent the weak convergence of the estimator has been derived which can be used for testing the null hypothesis of symmetry against this one sided alternative it also turns out that the same procedure can be used to estimate two cumulative incidence functions in a competing risks problem under the restriction that the cause specific hazard rates are ordered we also provide some real life examples

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

asymptotic behavior of the gibbs sampler mild sufficient conditions for the ergodicity of the gibbs sampler are obtained the geometric ergodicity of the gibbs sampler is then discussed where the main tool is the drift criterion this criterion requires the construction of a generalized energy function so that the chain is dissipating energy at a suitable rate whenever it lies outside the center of the state space for the two variable case a useful recipe is provided for constructing appropriate energy functions these results are illustrated with four examples

nonparametric estimation of a distribution subject to a stochastic precedence constraint for any two random variables x and y with distributions f and g defined on 0 x is said to stochastically precede y if p x y 1 2 for independent x and y stochastic precedence denoted by x spy is equivalent to e g x 1 2 the applicability of stochastic precedence in various statistical contexts including reliability modeling tests for distributional equality versus various alternatives and the relative performance of comparable tolerance bounds is discussed the problem of estimating the underlying distribution s of experimental data under the assumption that they obey a stochastic precedence sp constraint is treated in detail two estimation approaches one based on data shrinkage and the other involving data translation are used to construct estimators that conform to the sp constraint and each is shown to lead to a root n consistent estimator of the underlying distribution the asymptotic behavior of each of the estimators is fully characterized conditions are given under which

on the convergence of the markov chain simulation method the markov chain simulation method has been successfully used in many problems including some that arise in bayesian statistics we give a self contained proof of the convergence of this method in general state spaces under conditions that are easy to verify

estimation of a monotone mean residual life in survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age xmx defined by mx ex xx x where x is a lifetime m is called the mean residual life function in many applications it is reasonable to assume that m is decreasing dmrl or in creasing imrl we write decreasing increasing for nonincreasing non decreasing there is some literature on empirical estimators of m and their properties although tests for a monotone m are discussed in the literature we are not aware of any estimators of m under these order restrictions in this paper we initiate a study of such estimation our pro jection type estimators are shown to be strongly uniformly consistent on compact intervals and they are shown to be asymptotically root n equiv alent in probability to the unrestricted empirical estimator when m is strictly monotone thus the monotonicity is obtained free of charge at least in the aymptoticsense we also c onsider the nonparametricmaxi mum likelihood estimators they do not exist for the imrl case they do exist for the dmrl case but we have found the solutions to be too complex to be evaluated efficiently

monte carlo em estimation for time series models involving counts abstract the observations in parameter driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure these models result in very complex likelihoods and even the em algorithm which is usually well suited for problems of this type involves high dimensional integration in this article we discuss a monte carlo em mcem algorithm that uses a markov chain sampling technique in the calculation of the expectation in the e step of the em algorithm we propose a stopping criterion for the algorithm and provide rules for selecting the appropriate monte carlo sample size we show that under suitable regularity conditions an mcem algorithm will with high probability get close to a maximizer of the likelihood of the observed data we also discuss the asymptotic efficiency of the procedure we illustrate our monte carlo estimation method on a time series involving small counts the polio incidence time series previously analyzed by zeger

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

asymptotic upper bounds on the minimum distance of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of signal points in rn when a trellis code is used to encode data at the rate of k bits channel symbol each channel input depends not only on the most recent block of k bits to enter the encoder but will also depend on a set of bits preceding this block the bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state the performance of a trellis code depends on a suitably defined minimum distance property of that code this paper obtains upper bounds on this minimum distance that are better than any previously known

on estimating a survival curve subject to a uniform stochastic ordering constraint abstract if f and g are cumulative distribution functions on 0 governing the lifetimes of specific systems under study and if f and g are their corresponding survival functions then f is said to be uniformly stochastically smaller than g denoted by f 0 when f and g are absolutely continuous f g is equivalent to the assumption that the corresponding failure rates are ordered the applicability of the notion of uniform stochastic ordering in reliability and life testing is discussed given that a random sample x 1 x n of lifetimes has been obtained from f where f is assumed to satisfy the uniform stochastic ordering constraint f g where g is fixed and known the problem of estimating f is addressed it has been shown elsewhere that the method of nonparametric maximum likelihood estimation fails to provide consistent estimators in this type of

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

statistical inference for uniform stochastic ordering in several populations tion for k population problems under uniform stochastic ordering restrictions we derive closed form estimates even with right censored data by a reparameterization which reduces the problem to a well known isotonic regression problem we also derive the asymptotic distribution of the likelihood ratio statistic for testing equality of the k populations against the uniform stochastic ordering restriction this asymptotic distribution is of the chi bar square type as discussed by robertson wright and dykstra these distributional results are obtained by appealing to elegant results from empirical process theory and showing that the proposed test is asymptotically distribution free recurrence formulas are derived for the weights of the chi bar square distribution for particular cases the theory developed in this paper is illustrated by an example involving data for survival times for carcinoma of the oropharynx

adaptive bayesian multiuser detection for synchronous cdma with gaussian and impulsive noise we consider the problem of simultaneous parameter estimation and data restoration in a synchronous cdma system in the presence of either additive gaussian or additive impulsive white noise with unknown parameters the impulsive noise is modeled by a two term gaussian mixture distribution bayesian inference of all unknown quantities is made from the superimposed and noisy received signals the gibbs sampler a markov chain monte carlo procedure is employed to calculate the bayesian estimates the basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities adaptive bayesian multiuser detectors based on the gibbs sampler are derived for both the gaussian noise synchronous cdma channel and the impulsive noise synchronous cdma channel a salient feature of the proposed adaptive bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities and they produce as output the a posteriori symbol probabilities that is they are soft input soft output algorithms hence these methods are well suited for iterative processing in a coded system which allows the adaptive bayesian multiuser detector to refine its processing based on the information from the decoding stage and vice versa a receiver structure termed the adaptive turbo multiuser detector

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea