robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

finite state automata representing two dimensional subshifts a new type of two dimensional automaton has been defined to recognize a class of two dimensional shifts of finite type having the property that every admissible block found within the related local picture language can be extended to a point of the subshift here it is shown that this automaton accurately represents the image of the represented two dimensional shift of finite type under a block code it is then shown that these automata can be used to check for a certain type of two dimensional transitivity in the factor language of the corresponding shift space and how this relates to periodicity in the two dimensional case the paper closes with a notion of follower sets that are used to reduce the size of the automata representing two dimensional sofic shifts

estimation in covariance components models abstract estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes the estimation of fixed and random effects when the variances and covariances are known is presented in bayesian terms point estimates of the unknown variances and covariances are computed using the em algorithm for maximum likelihood estimation from incomplete data the techniques are illustrated with data on law schools field mice and professional football teams

small area estimation when auxiliary information is measured with error summary small area estimation methods typically combine direct estimates from a survey with pre dictions from a model in order to obtain estimates of population quantities with reduced mean squared error when the auxiliary information used in the model is measured with error using a small area estimator such as the fay herriot estimator while ignoring measurement error may be worse than simply using the direct estimator we propose a new small area estimator that accounts for sampling variability in the auxiliary information and derive its properties in particular show ing that it is approximately unbiased the estimator is applied to predict quantities measured in the u s national health and nutrition examination survey with auxiliary information from the u s national health interview survey

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

empirical bayes estimation in finite population sampling abstract empirical bayes methods are becoming increasingly popular in statistics robbins 1955 introduced the method in the context of nonparametric estimation of a completely unspecified prior distribution subsequently the method has been explored very successfully in a series of articles by efron and morris 1973 1975 1977 in a parametric framework in the efron morris setup a family of parametric distributions is used as possible priors but only when one or more of the parameters of the family of prior distributions is estimated from the data morris 1983 listed a number of areas where empirical bayes methods are used one of the main features of empirical bayes analysis is to borrow strength from the ensemble that is use information from similar sources in constructing estimators and predictors in addition to the most directly available source of information there are some situations in finite population sampling where such methods might be suitable for instance in many repetitive surve

mean squared error estimation in transformed fay herriot models summary the problem of accurately estimating the mean squared error of small area estimators within a fay herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable for bias corrected empirical best linear unbiased predictor small area point estimators mean squared error formulae and estimators are provided with biases of smaller order than the reciprocal of the number of small areas the performance of these mean squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the us census bureau s on going small area income and poverty estimation project

survival and residence times in disordered chains with bias we present a unified framework for first passage time and residence time of random walks in finite one dimensional disordered biased systems the derivation is based on the exact expansion of the backward master equation in cumulants the dependence on the initial condition system size and bias strength is explicitly studied for models with weak and strong disorders application to thermally activated processes is also developed

mean first passage and residence times of random walks on asymmetric disordered chains an algebraic derivation is presented which yields the exact solution of the mean first passage and mean residence times of a one dimensional asymmetric random walk for quenched disorder two models of disorder are analytically treated both absorbing absorbing and reflecting absorbing boundaries are considered particularly the interplay between asymmetry and disorder is studied

first passage probability of a random walk on a disordered one dimensional lattice a method is presented which yields the exact solution of the generating function for the first passage probability and related observables for a one dimensional random walk with random hopping rates on each site a geometrical and statistical mechanical interpretation of the problem is suggested and is used for obtaining the asymptotic properties of the occupation and first passage probabilities the class of values with the property of self averaging is found

on the entropy of zd subshifts of finite type abstract in this paper we study the combinatorial the topological and the periodic entropies of z d subshifts of finite type we show that the combinatorical and the topological entropies are equal we give sufficient conditions for the periodic entropy to be equal to the topological entropy

c algebras associated with hilbert c quad modules of c textile dynamical systems abstract a c textile dynamical system a consists of a unital c algebra a two families of endomorphisms and a a of a and certain commutation relations among them it yields a two dimensional subshift and a multistructure hilbert c bimodule which we call a hilbert c quad module we introduce a c algebra from the hilbert c quad module as a two dimensional analogue of pimsner s construction of c algebras from hilbert c bimodules we study the c algebras defined by the hilbert c quad modules and prove that they have universal properties subject to certain operator relations we also present examples arising from commuting matrices

sumca simple unified monte carlo assisted approach to second order unbiased mean squared prediction error estimation we propose a simple unified monte carlo assisted approach called sumca to second order unbiased estimation of the mean squared prediction error mspe of a small area predictor the mspe estimator proposed is easy to derive has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor empirical best predictor and post model selection empirical best linear unbiased predictor and empirical best predictor as special cases furthermore the leading term of the mspe estimator proposed is guaranteed positive the lower order term corresponds to a bias correction which can be evaluated via a monte carlo method the computational burden for the monte carlo evaluation is much less compared with other monte carlo based methods that have been used for producing second order unbiased mspe estimators such as the double bootstrap and monte carlo jackknife the sumca estimator also has a nice stability feature theoretical and empirical results demonstrate properties and advantages of the sumca estimator

mean squared error of empirical predictor the term empirical predictor refers to a two stage predictor of a linear combination of fixed and random effects in the first stage a predictor is obtained but it involves unknown parameters thus in the second stage the unknown parameters are replaced by their estimators in this paper we consider mean squared errors mse of empirical predictors under a general setup where ml or reml estimators are used for the second stage we obtain second order approximation to the mse as well as an estimator of the mse correct to the same order the general results are applied to mixed linear models to obtain a second order approximation to the mse of the empirical best linear unbiased predictor eblup of a linear mixed effect and an estimator of the mse of eblup whose bias is correct to second order the general mixed linear model includes the mixed anova model and the longitudinal model as special cases

entropy of bit stuffing induced measures for two dimensional checkerboard constraints a modified bit stuffing scheme for two dimensional 2 d checkerboard constraints is introduced the entropy of the scheme is determined based on a probability measure defined by the modified bit stuffing entropy results of the scheme are given for 2 d constraints on a binary alphabet the constraints considered are 2 d rll d infin for d 2 3 and 4 as well as for the constraint with a minimum 1 norm distance of 3 between 1s for these results the entropy is within 1 2 of an upper bound on the capacity for the constraint as a variation of the scheme periodic merging arrays are also considered

enumeration of simple random walks and tridiagonal matrices we present some old and new results in the enumeration of random walks in one dimension mostly developed in work on enumerative combinatorics the relation between the trace of the nth power of a tridiagonal matrix and the enumeration of weighted paths of n steps allows an easier combinatorial enumeration of paths it also seems promising for the theory of tridiagonal random matrices

distribution functions for random walk processes on networks an analytic method a novel analytic method for deriving and analyzing probability distribution functions of variables arising in random walk problems is presented applications of the method to quasi one dimensional systems show that the generating functions of interest possess simple poles and no branch cuts outside the unit complex disk this fact makes it possible to derive closed formulas for the full probability distribution functions and to analyze their properties we find that transverse structures attached to a one dimensional backbone can be responsible for the appearance of power laws in observables such as the distribution of first arrival times or the total current moving through a model photoexcited dirty semiconductor our results compare well with experiment we conclude that in some cases a geometrical effect e g that of a transverse structure may be indistinguishable from a dynamical effect long waiting time we also find universal shapes of distribution functions humped structures which are not characterized by power laws the role of bias in determining properties of quasi one dimensional structures is examined a master equation for generating functions is derived and applied to the computation of currents our method is also applied to a fractal structure yielding nontrivial power laws in all finite networks considered all probability distributions decay exponentially for asymptotically long times

comparisons of alternative predictors under the balanced one way random model abstract prediction of an arbitrary linear combination of the random effects of a balanced one way random model is investigated alternative two stage predictors are compared on the basis of their conditional on the random effects and unconditional bias and mean squared errors when the true value of the ratio of expected mean squares is known there exists a best linear unbiased predictor blup when the true value is unknown a two stage predictor obtained from the blup by replacing the true value with an estimated value can be used when the ratio of expected mean squares is estimated by maximum likelihood bayesian methods or various related methods a two stage predictor is obtained whose properties compare favorably with for example those of the least squares predictor and the positive part james stein predictor

decidability of irreducible tree shifts of finite type we reveal an algorithm for determining the complete prefix code irreducibility cpc irreducibility of dyadic trees labeled by a finite alphabet by introducing an extended directed graph representation of tree shift of finite type tsft we show that the cpc irreducibility of tsfts is related to the connectivity of its graph representation which is a similar result to one dimensional shifts of finite type

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

c algebras and fell bundles associated to a textile system abstract the notion of textile system was introduced by m nasu in order to analyze endomorphisms and automorphisms of topological markov shifts a textile system is given by two finite directed graphs g and h and two morphisms p q g h with some extra properties it turns out that a textile system determines a first quadrant two dimensional shift of finite type via a collection of wang tiles and conversely any such shift is conjugate to a textile shift in the case the morphisms p and q have the path lifting property we prove that they induce groupoid morphisms g h between the corresponding etale groupoids of g and h we define two families a m n and a m n of c algebras associated to a textile shift and compute them in specific cases these are graph algebras associated to some one dimensional shifts of finite type constructed from the textile shift under extra hypotheses we also define two families of fell bundles which encode the complexity of these two dimensional shifts we consider several classes of examples of textile shifts including the full shift the golden mean shift and shifts associated to rank two graphs

random walkers in one dimensional random environments exact renormalization group analysis sinai s model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields exact results at long times the effects of an additional small uniform bias force are also studied we obtain analytically the scaling form of the distribution of the position x t of a particle the probability of it not returning to the origin and the distributions of first passage times in an infinite sample as well as in the presence of a boundary and in a finite but large sample we compute the distribution of the meeting time of two particles in the same environment we also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward these quantities obey multifractal scaling characterized by generalized persistence exponents ensuremath theta g which we compute in the presence of a small bias the number of returns to the origin becomes finite characterized by a universal scaling function which we obtain the full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained as well as detailed analytical information about correlations between directions and times of successive jumps the two time distribution of the positions of a particle x t and x t ensuremath with tg t ensuremath is also computed exactly it is found to exhibit aging with several time regimes characterized by different behaviors in the unbiased case for t ensuremath t ensuremath ensuremath sim t ensuremath ensuremath alpha with ensuremath alpha g1 it exhibits a mathrm ln t mathrm ln t ensuremath scaling with a singularity at coinciding rescaled positions x t x t ensuremath this singularity is a novel feature and corresponds to particles that remain in a renormalized valley for closer times ensuremath alpha l1 the two time diffusion front exhibits a quasiequilibrium regime with a mathrm ln t ensuremath t ensuremath mathrm ln t ensuremath behavior which we compute the crossover to a t t ensuremath aging form in the presence of a small bias is also obtained analytically rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail connections with the green function of a one dimensional schr odinger problem and quantum spin chains are discussed

mixing properties of tree shifts the uncertainty of multidimensional shift spaces draws attracted attention of researchers for example the emptiness problem is undecidable there exist aperiodic shifts of finite type there is a nonempty shift of finite type exhibiting nonextensible local patterns this paper investigates symbolic dynamics on cayley trees and gives affirmative answers to the above questions in tree shifts beyond that with introducing block gluing tree shift a sufficient condition of exhibiting positive topological entropy is revealed