second order asymptotics for the gaussian mac with degraded message sets this paper studies the second order asymptotics of the gaussian multiple access channel with degraded message sets for a fixed average error probability varepsilon in 0 1 and an arbitrary point on the boundary of the capacity region we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than varepsilon as a stepping stone to this local notion of the second order asymptotics we study a global notion and establish relationships between the two we provide a numerical example to illustrate how the angle of approach to a boundary point affects the second order coding rate this is the first conclusive characterization of the second order asymptotics of a network information theory problem in which the capacity region is not a polygon

common message broadcast channels with feedback in the nonasymptotic regime full feedback we investigate the maximum coding rate for a given average blocklength and error probability over a k user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable length stop feedback codes for the point to point case polyanskiy et al 2011 demonstrated that variable length coding combined with stop feedback significantly increases the speed of convergence of the maximum coding rate to capacity this speed up manifests itself in the absence of a square root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths i e zero dispersion in this paper we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common message k user discrete memoryless broadcast channel which strengthen and generalize the ones reported in trillingsgaard et al 2015 for the two user case an asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common message broadcast channels e g the binary symmetric broadcast channel furthermore we identify conditions under which our converse and achievability bounds are tight up to the second order through numerical evaluations we illustrate that our second order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point to point case

on latin hypercube sampling this paper contains a collection of results on latin hypercube sampling the first result is a berry esseen type bound for the multivariate central limit theorem of the sample mean hat mu n based on a latin hypercube sample the second establishes sufficient conditions on the convergence rate in the strong law for hat mu n finally motivated by the concept of empirical likelihood a way of constructing nonparametric confidence regions based on latin hypercube samples is proposed for vector means

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

on fuzzy syntopogenous structures and preorder abstract in this paper we combine fuzzy topological structure on x with algebraic structure on x and investigate their corresponding structures and their properties first we study the preorder relation generated by an l fuzzy syntopogenous structure conversely we research the l fuzzy syntopogenous structure defined by a preorder relation second we define increasing decreasing l fuzzy syntopogenous spaces with preorder and study some properties of them finally we give an important example of increasing l fuzzy syntopogenous space i e r s r

multivariate approximations in wasserstein distance by stein s method and bismut s formula stein s method has been widely used for probability approximations however in the multi dimensional setting most of the results are for multivariate normal approximation or for test functions with bounded second or higher order derivatives for a class of multivariate limiting distributions we use bismut s formula in malliavin calculus to control the derivatives of the stein equation solutions by the first derivative of the test function combined with stein s exchangeable pair approach we obtain a general theorem for multivariate approximations with near optimal error bounds on the wasserstein distance we apply the theorem to the unadjusted langevin algorithm

stein s method and a quantitative lindeberg clt for the fourier transforms of random vectors abstract we use a multivariate version of stein s method to establish a quantitative lindeberg clt for the fourier transforms of random n vectors we achieve this conceptually mainly by constructing a natural approach structure on n random vectors overlying the topology of weak convergence and technically mainly by deducing a specific integral representation for the hessian matrix of a solution to the stein equation with test function e t x exp i k 1 n t k x k where t x r n

a berry esseen bound for symmetric statistics the rate of convergence of the distribution function of a symmetric function of n independent and identically distributed random variables to its normal limit is investigated under appropriate moment conditions the rate is shown to be o left n frac 1 2 right this theorem generalizes many known results for special cases and two examples are given possible further extensions are indicated

syntopogenous structure on completely distributive lattice and its connectedness abstract in this paper the general theory of syntopogenous structures on completely distributive lattices is established the unified question of cotopology quasi uniformity and t structure is investigated the results of this paper complete the framework of the topological structure on completely distributive lattices and generalize the corresponding theory in general and fuzzy topology finally we examine the connectedness the following main results about connectedness are obtained 1 1 if f l1 s1 l2 s2 is an s1 s2 continuous goh function and d l1 is s1 connected element then f d is s2 connected element 2 2 let c l s be an s connected element and c d c then d is an s connected element 3 3 i li si is connected iff for any i i li si is connected

stein s method for diffusion approximations stein s method of obtaining distributional approximations is developed in the context of functional approximation by the wiener process and other gaussian processes an appropriate analogue of the one dimensional stein equation is derived and the necessary properties of its solutions are established the method is applied to the partial sums of stationary sequences and of dissociated arrays to a process version of the wald wolfowitz theorem and to the empirical distribution function

on steinʼs method for infinite dimensional gaussian approximation in abstract wiener spaces abstract in this paper we generalize stein s method to infinite variate normal approximation that is an infinite dimensional approximation by abstract wiener measures on a real separable banach space we first establish a stein s identity for abstract wiener measures and solve the corresponding stein s equation then we will present a gaussian approximation theorem using exchangeable pairs in an infinite variate context as an application we will derive an explicit error bound of gaussian approximation to the distribution of a sum of independent and identically distributed banach space valued random variables based on a lindeberg levy type limit theorem in addition an analogous of berry esseen type estimate for abstract wiener measures will be obtained

non normal limiting distribution for optimal alignment scores of strings in binary alphabets we consider two independent binary i i d random strings x and y of equal length n and the optimal alignments according to a symmetric scoring functions only we decompose the space of scoring functions into five components two of these components add a part to the optimal score which does not depend on the alignment and which is asymptotically normal we show that when we restrict the number of gaps sufficiently and add them only into one sequence then the alignment score can be decomposed into a part which is normal and has order o sqrt n and a part which is on a smaller order and tends to a tracy widom distribution adding gaps only into one sequence is equivalent to aligning a string with its descendants in case of mutations and deletes for testing relatedness of strings the normal part is irrelevant since it does not depend on the alignment hence it can be safely removed from the test statistic

open t j chain with boundary impurities we study integrable boundary conditions for the supersymmetric t j model of correlated electrons which arise when combining static scattering potentials with dynamical impurities carrying an internal degree of freedom the latter differ from the bulk sites by allowing for double occupation of the local orbitals the spectrum of the resulting hamiltonians is obtained by means of the algebraic bethe ansatz

a berry esseen bound for functions of independent random variables the rate of convergence in the central limit theorem for functions of independent random variables is studied in a unifying approach the basic result sharpens and extends a theorem of van zwet applications to u l and r statistics are also given improving or extending the results of helmers and van zwet helmers and huskova does and van es and helmers

central limit theorems and bootstrap in high dimensions this paper derives central limit and bootstrap theorems for probabilities that sums of centered high dimensional random vectors hit hyperrectangles and sparsely convex sets specifically we derive gaussian and bootstrap approximations for probabilities p n 1 2 ni 1xi a p n 1 2 i 1nxi a where x1 xnx1 xn are independent random vectors in rprp and aa is a hyperrectangle or more generally a sparsely convex set and show that the approximation error converges to zero even if p pn p pn as n n and p np n in particular pp can be as large as o ecnc o ecnc for some constants c c 0c c 0 the result holds uniformly over all hyperrectangles or more generally sparsely convex sets and does not require any restriction on the correlation structure among coordinates of xixi sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend only on a small subset of their arguments with hyperrectangles being a special case

an edgeworth expansion for symmetric statistics we consider asymptotically normal statistics which are symmetric functions of n i i d random variables for these statistics we prove the validity of an edgeworth expansion with remainder o n 1 under cramer s condition on the linear part of the statistic and moment assumptions for all parts of the statistic by means of a counterexample we show that it is generally not possible to obtain an edgeworth expansion with remainder o n 1 without imposing additional assumptions on the structure of the nonlinear part of the statistic

on the rate of convergence in the multivariate clt berry esseen theorems are proved in the multidimensional central limit theorem without using fourier methods an effective and simple estimate of the error in the clt for sums and convex sets using stein s method and induction is derived furthermore the error in the clt for multivariate functions of independent random elements is estimated extending results of van zwet and friedrich to the multivariate case

on convexity of fuzzy syntopogenous spaces in this paper we combine fuzzy syntopogenous structures with algebraic on x and look for their corresponding structures and typical properties first the increasing and decreasing spaces have been studied and an important example r sr has been given theorem 3 10 second two general types of convexity on l fuzzy syntopogenous structures x s have been defined the examples of them have been given and their relationship has been investigated third the equivalent description of convexity have been given finally a sequence of important properties of convexity have been obtained

stein s method on wiener chaos we combine malliavin calculus with stein s method in order to derive explicit bounds in the gaussian and gamma approximations of random variables in a fixed wiener chaos of a general gaussian process our approach generalizes refines and unifies the central and non central limit theorems for multiple wiener ito integrals recently proved in several papers from 2005 to 2007 by nourdin nualart ortiz latorre peccati and tudor we apply our techniques to prove berry esseen bounds in the breuer major clt for subordinated functionals of fractional brownian motion by using the well known mehler s formula for ornstein uhlenbeck semigroups we also recover a technical result recently proved by chatterjee concerning the gaussian approximation of functionals of finite dimensional gaussian vectors

the berry esseen bound for studentized statistics we derive berry esseen bounds for a class of studentized statistics the results are applied to studentized ustatistics studentized l statistics and studentized functions of the sample mean to give the berry esseen bounds under conditions weaker than those obtained by alternative methods

bootstrap confidence sets under model misspecification a multiplier bootstrap procedure for construction of likelihood based confidence sets is considered for finite samples and a possible model misspecification theoretical results justify the bootstrap consistency for a small or moderate sample size and allow to control the impact of the parameter dimension p the bootstrap approximation works if p n is small the main result about bootstrap consistency continues to apply even if the underlying parametric model is misspecified under the so called small modeling bias condition in the case when the true model deviates significantly from the considered parametric family the bootstrap procedure is still applicable but it becomes a bit conservative the size of the constructed confidence sets is increased by the modeling bias we illustrate the results with numerical examples for misspecified constant and logistic regressions jel classification codes c13 c15

a multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments let f 0 1 d r be an integrable function an objective of many computer experiments is to estimate 0 1 d f x dx by f x dx by evaluating f at a finite number of points in 0 1 d there is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays this article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs owen statist sinica 2 1992a 439 452 as well as for a class of oa based latin hypercubes tang j amer statist assoc 81 1993 1392 1397

sur le theoreme de berry esseen pour les suites faiblement dependantes nous etendons la methode de demonstration du theoreme de berry esseen proposee par bergstrom aux suites de variables aleatoires faiblement dependantes en particulier nous montrons que pour les suites stationnaires de variables aleatoires reelles bornees la vitesse de convergence dans le theoreme limite central en distance de levy est de l ordre den 1 2 des que la suite p p 0 des coefficients de melange uniforme satisfait la condition p 0 p p

invariance principles for homogeneous sums universality of gaussian wiener chaos we compute explicit bounds in the normal and chi square approximations of multilinear homogenous sums of arbitrary order of general centered independent random variables with unit variance in particular we show that chaotic random variables enjoy the following form of universality a the normal and chi square approximations of any homogenous sum can be completely characterized and assessed by first switching to its wiener chaos counterpart and b the simple upper bounds and convergence criteria available on the wiener chaos extend almost verbatim to the class of homogeneous sums

a high dimensional clt in mathcal w _2 w 2 distance with near optimal convergence rate let x 1 ldots x n be i i d random vectors in mathbb r d with vert x 1 vert le beta then we show that begin aligned frac 1 sqrt n left x 1 cdots x n right end aligned converges to a gaussian in quadratic transportation also known as kantorovich or wasserstein distance at a rate of o left frac sqrt d beta log n sqrt n right improving a result of valiant and valiant the main feature of our theorem is that the rate of convergence is within log n of optimal for n d rightarrow infty

compound poisson approximation for nonnegative random variables via stein s method the aim of this paper is to extend stein s method to a compound poisson distribution setting the compound poisson distributions of concern here are those of the form pois nu where nu is a finite positive measure on 0 infty a number of results related to these distributions are established these in turn are used in a number of examples to give bounds for the error in the compound poisson approximation to the distribution of a sum of random variables

entropy and the fourth moment phenomenon we develop a new method for bounding the relative entropy of a random vector in terms of its stein factors our approach is based on a novel representation for the score function of smoothly perturbed random variables as well as on the de bruijn s identity of information theory when applied to sequences of functionals of a general gaussian field our results can be combined with the carbery wright inequality in order to yield multidimensional entropic rates of convergence that coincide up to a logarithmic factor with those achievable in smooth distances such as the 1 wasserstein distance in particular our findings settle the open problem of proving a quantitative version of the multidimensional fourth moment theorem for random vectors having chaotic components with explicit rates of convergence in total variation that are independent of the order of the associated wiener chaoses the results proved in the present paper are outside the scope of other existing techniques such as for instance the multidimensional stein s method for normal approximations

a case where interference does not affect the channel dispersion in 1975 carleial presented a special case of an interference channel called the very strong interference regime in which the interference does not reduce the capacity of the constituent point to point gaussian channels in this paper we show that in the strictly very strong interference regime the dispersions are similarly unaffected more precisely in this paper we characterize the second order coding rates of the gaussian interference channel in the strictly very strong interference regime in other words we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the rectangular capacity region these second order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the single user gaussian channel this allows us to conclude that the dispersions are unaffected by interference in this channel model