further relaxations of the semidefinite programming approach to sensor network localization recently a semidefinite programming sdp relaxation approach has been proposed to solve the sensor network localization problem although it achieves high accuracy in estimating the sensor locations the speed of the sdp approach is not satisfactory for practical applications in this paper we propose methods to further relax the sdp relaxation more precisely to relax the single semidefinite matrix cone into a set of small size semidefinite submatrix cones which we call a sub sdp ssdp approach we present two such relaxations although they are weaker than the original sdp relaxation they retain the key theoretical property and numerical experiments show that they are both efficient and accurate the speed of the ssdp is even faster than that of other approaches based on weaker relaxations the ssdp approach may also pave a way to efficiently solving general sdp problems without sacrificing the solution quality

saddlepoint approximation for student s t statistic with no moment conditions a saddlepoint approximation of the student s t statistic was derived by daniels and young biometrika 78 1991 169 179 under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a normal density in the tails this is a severe restriction on the approximation s applicability in this paper we show that this strong exponential moment restriction can be completely dispensed with that is saddlepoint approximation of the student s t statistic remains valid without any moment condition this confirms the folklore that the student s t statistic is robust against outliers the saddlepoint approximation neat only provides a very accurate approximation for the student s t statistic but it also can be applied much more widely in statistical inference as a result saddlepoint approximations should always be used whenever possible some numerical work will be given to illustrate these points

saddlepoint expansions in finite population problems summary saddlepoint approximations are derived for the sample mean in the case where samples are obtained randomly without replacement from a finite population asymptotic properties are investigated the great accuracy is demonstrated by numerical examples extensions to more general statistics are discussed

approximations of marginal tail probabilities and inference for scalar parameters summary in many situations inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density for such inference accurate approximations of marginal tail probabilities are useful to avoid high dimensional integrals two tail probability approximations are developed in this paper numerical results given for conditional inference in location scale and linear regression models show the approximations to be generally accurate even for small sample sizes

statistical thermodynamics for choice models on graphs abstract formalism based on equilibrium statistical thermodynamics is applied to communication networks of decision making individuals it is shown that in statistical ensembles for choice models properly defined disutility plays the same role as energy in statistical mechanics we demonstrate additivity and extensivity of disutility and build three types of equilibrium statistical ensembles the canonical the grand canonical and the super canonical using boltzmann probability measure one can reproduce the logit choice model we propose using q distributions for temperature evolution of moments of stochastic variables the formalism is applied to networks with fixed topologies of different degrees of symmetry for which analytic and numerical results are presented

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

the evolutionary minority game with local coordination abstract we discuss a modification of the evolutionary minority game emg in which agents are placed in the nodes of a regular or a random graph a neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision depending upon her neighborhood we report numerical results for the topologies of a ring a torus and a random graph changing the size of the neighborhood we find the surprising result that in the emg a better coordination a lower frustration can be achieved if agents base their actions on local information disregarding the global trend in the self segregation process

towards a universal self normalized moderate deviation this paper is an attempt to establish a universal moderate deviation for self normalized sums of independent and identically distributed random variables without any moment condition the exponent term in the moderate deviation is specified when the distribution is in the centered feller class an application to the law of the iterated logarithm is given

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

on distributions of ratios a large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables if the denominator variable is positive then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables if in addition the joint characteristic function of numerator and denominator is known then standard fourier inversion techniques can be used to reconstruct the distribution function from it most research in this field has been based on this correspondence but which breaks down when both numerator and denominator are supported on the entire real line the present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case and reduce to known results when the denominator is almost surely positive applications include the iv est imator of a structural parameter in a just identified equation

miscellanea inference on rare errors using asymptotic expansions and bootstrap calibration summary the number of items in error in an audit population is usually quite small whereas the error distribution is typically highly skewed to the right for applications in statistical auditing where line item sampling is appropriate a new upper confidence limit for the total error amount in an audit population is obtained our method involves an empirical cornish fisher expansion in the first stage in the second stage we employ the bootstrap to calibrate the coverage probability of the resulting interval estimate

saddlepoint approximation for moment generating functions of truncated random variables we consider the problem of approximating the moment generating function mgf of a truncated random variable in terms of the mgf of the underlying i e untruncated random variable the purpose of approximating the mgf is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables two important statistical applications are the following the approximation of certain multivariate cumulative distribution functions and the approximation of passage time distributions in ion channel models which incorporate time interval omission we derive two types of representation for the mgf of a truncated random variable one of these representations is obtained by exponential tilting the second type of representation which has two versions is referred to as an exponential convolution representation each representation motivates a different approximation it turns out that each of the three approximations is extremely accurate in those cases to which it is suited moreover there is a simple rule of thumb for deciding which approximation to use in a given case and if this rule is followed then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate

a weighted bootstrap approach to bootstrap iteration the operation of resampling from a bootstrap resample encountered in applications of the double bootstrap may be viewed as resampling directly from the sample but using probability weights that are proportional to the numbers of times that sample values appear in the resample this suggests an approximate approach to double bootstrap monte carlo simulation where weighted bootstrap methods are used to circumvent much of the labour involved in compounded monte carlo approximation in the case of distribution estimation or equivalently confidence interval calibration the new method may be used to reduce the computational labour moreover the method produces the same order of magnitude of coverage error for confidence intervals or level error for hypothesis tests as a full application of the double bootstrap

an almost sure central limit theorem for self normalized partial sums let x i i 1 be a sequence of i i d random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance denote s email protected i 1 nx i v n email protected i 1 nx i 2 then an almost sure central limit theorem for self normalized partial sums s n v n is studied under a mild condition in this paper

saddlepoint approximations for the difference of order statistics and studentized sample quantiles summary for a sample from a given distribution the difference of two order statistics and the studentized quantile are statistics whose distribution is needed to obtain tests and confidence intervals for quantiles and quantile differences this paper gives saddlepoint approximations for densities and saddlepoint approximations of the lugannani rice form for tail probabilities of these statistics the relative errors of the approximations are n i uniformly in a neighbourhood of the parameters and this uniformity is global if the densities are log concave

cooperative wireless sensor network positioning via implicit convex feasibility we propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions based on a geometric interpretation we formulate the positioning problem as an implicit convex feasibility problem in which some of the sets depend on the unknown target positions and apply a parallel projection onto convex sets approach to estimate the unknown target node positions the proposed technique is suitable for parallel implementation in which every target node in parallel can update its position and share the estimate of its location with other targets we mathematically prove convergence of the proposed algorithm simulation results reveal enhanced performance for the proposed approach compared to available techniques based on projections especially for sparse networks

edgeworth expansions of suitably normalized sample mean statistics for atomic markov chains this paper is devoted to the problem of estimating functionals of type f fd from observations drawn from a positive recurrent atomic markov chain open image in new window with stationary distribution the properties of different estimators are studied beyond an accurate estimation of their bias the estimation of their asymptotic variance is considered we also show that the results of malinovskii 1987 on the validity of the formal edgeworth expansion for sample mean statistics of type t n n 1 n i 1 f x i extend to their studentized versions normalized by the asymptotic variance estimates we consider

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

periodic attractors of random truncator maps this paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system we represent the symbolic dynamics generated by this system as a non commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure a stochastic model is constructed on these endomorphisms which leads to the classification of the distribution of periodic orbits for random truncator maps this framework is applied to investigate the periodic transitions of bornholdt s spin market model

an exponential nonuniform berry esseen bound for self normalized sums in this paper we shall derive exponential nonuniformberry esseen bounds in the central limit theorem for self normalized sums we show that the size of the error can be reduced considerably by replacing the usual standardization by self normalization in particular we establish the exponential bounds for the probability of the self normalized sums under the condition that the third moment is finite whereas an exponential moment assumption is required for the standardized sums applications to t statistics and the probabilities of moderate deviations of self normalized sums are also discussed

exact inequalities for sums of asymmetric random variables with applications let rm bs 1 dots rm bs n be independent identically distributed random variables each having the standardized bernoulli distribution with parameter p in 0 1 let m p 1 p 2 p 2 2 sqrt p p 2 4 p 2 if 0 p le frac12 and m p 1 if frac12 le p 1 let m ge m p let f be such a function that f and f are nondecreasing and convex then it is proved that for all nonnegative numbers c 1 dots c n one has the inequality mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n le mathsf e f big s m mathrm b s 1 dots mathrm bs n big where s m big frac1n sum i 1 n c i 2m big frac1 2m the lower bound m p on m is exact for each p in 0 1 moreover operatorname mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n is schur concave in c 1 2m ldots c n 2m

bounds for probabilities of small relative errors for empirical saddlepoint and bootstrap tail approximations to obtain test probabilities based on empirical approximations to the distribution of a studentized function of a mean we need the approximations to be accurate with sufficiently high probability in particular when these test probabilities are small it is best to consider relative errors here we show that in the case of univariate standardized means and in the general case of tests based on smooth functions of means the empirical approximations have asymptotically small relative errors on sets with probability differing from 1 by an exponentially small quantity and that these error rates hold for moderately large deviations in particular for standardized deviations of order n 1 6 the probabilities approximated are exponentially small with exponents of order n 1 3 and the corresponding relative errors tend to zero on sets whose complements have probabilities of the order of the probabilities being approximated

when is the student t statistic asymptotically standard normal let x x i i in mathbb n be independent identically distributed random variables it is shown that the student t statistic based upon the sample x i i 1 n is asymptotically n 0 1 if and only if x is in the domain of attraction of the normal law it is also shown that for any x if the self normalized sums u n sum i 1 n x i sum i 1 n x i 2 1 2 n in mathbb n are stochastically bounded then they are uniformly subgaussian that is sup n mathbb e exp lambda u n 2 infty for some lambda 0

on energy based acoustic source localization for sensor networks in this paper energy based localization methods for source localization in sensor networks are examined the focus is on least squares based approaches due to a good tradeoff between performance and complexity a suite of methods are developed and compared first two previously proposed methods quadratic elimination and one step are shown to yield the same location estimate for a source next it is shown that as the errors which perturb the least squares equations are nonidentically distributed it is more appropriate to consider weighted least squares methods which are observed to yield significant performance gains over the unweighted methods finally a new weighted direct least squares formulation is presented and shown to outperform the previous methods with much less computational complexity unlike the quadratic elimination method the weighted direct least squares method is amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains for a sufficiently large number of samples simulations show that the weighted direct solution with correction wdc can be more accurate with significantly less computational complexity than the maximum likelihood estimator and approaches cramer rao bound crb furthermore it is shown that wdc attains crb for the case of a white source

exact and approximate solutions of source localization problems we consider least squares ls approaches for locating a radiating source from range measurements which we call r ls or from range difference measurements rd ls collected using an array of passive sensors we also consider ls approaches based on squared range observations sr ls and based on squared range difference measurements srd ls despite the fact that the resulting optimization problems are nonconvex we provide exact solution procedures for efficiently computing the sr ls and srd ls estimates numerical simulations suggest that the exact sr ls and srd ls estimates outperform existing approximations of the sr ls and srd ls solutions as well as approximations of the r ls and rd ls solutions which are based on a semidefinite relaxation

approximate marginal densities of nonlinear functions this paper presents an asymptotic approximation for the marginal density of a nonlinear function g 0 that is applicable when the joint density of 0 is dominated by a single mode and the jacobian of g is of full rank near that mode the approximation is based on laplace s method and its asymptotic properties are similar to those of the saddlepoint approximation the approximation is applied to the computation of a marginal posterior density a marginal sampling density and a marginal density based on a multivariate saddlepoint approximation to a joint density

saddlepoint approximations for marginal and conditional probabilities of transformed variables the lugannani and rice formula for tail areas in the univariate case has recently been extended to tail areas for marginal distributions and for conditional distributions in certain multivariate settings however the results on relative order of errors are given only formally or under the strong continuity assumptions necessary to obtain density approximations this paper attempts to give a unified treatment of these results for smooth transformations of multivariate means under weaker conditions appropriate to indirect edgeworth approximations for probabilities

second order cone programming relaxation of sensor network localization the sensor network localization problem has been much studied recently biswas and ye proposed a semidefinite programming sdp relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed here we study a second order cone programming socp relaxation of this problem motivated by its simpler structure and its potential to be solved faster than sdp we show that the socp relaxation though weaker than the sdp relaxation has nice properties that make it useful as a problem preprocessor in particular sensors that are uniquely positioned among interior solutions of the socp relaxation are accurate up to the square root of the distance error thus these sensors which are easily identified are accurately positioned in our numerical simulation the interior solution found can accurately position up to 80 90p of the sensors we also propose a smoothing coordinate gradient descent method for finding an interior solution that is faster than an interior point method

uniform coverage bounds for confidence intervals and berry esseen theorems for edgeworth expansion we derive upper bounds for the coverage error of confidence intervals for a population mean uniformly over large classes of populations and different types of confidence intervals it is shown that the order of these bounds is achieved by the normal approximation method for constructing confidence intervals uniformly over distributions with finite third moment and by an empirical edgeworth correction of this approach uniformly over smooth distributions with finite fourth moments these results have straightforward extensions to higher orders of edgeworth correction and higher orders of moments our upper bounds to coverage accuracy are based on berry esseen theorems for edgeworth expansions of the distribution of the studentized mean

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

bayesian marginal inference abstract a method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite possibly tedious numerical integrations are replaced by conditional maximizations which are shown to be quite accurate in a number of special cases there are similarities with the profile likelihood ideas originated by kalbfleisch and sprott 1970 and the method is contrasted with a laplacian approximation recommended by kass tierney and kadane 1988 in press referred to here as the ktk procedure the methods are used to approximate the marginal posterior densities of the log linear interaction effects and an overall measure of association in a two way contingency table snee s 1974 hair eye color data are reanalyzed and adjustments are proposed to goodman s 1964 analysis for the full rank interaction model another application concerns marginaliz

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

edgeworth expansion for student s t statistic under minimal moment conditions recent advances in the theory of edgeworth expansion allow rigorous estimation of remainder terms under explicit regularity conditions however even in the important case of student s t statistic the moment conditions required are unrealistically stringent in this note we relax those conditions to the minimum needed to define terms in the edgeworth expansion

on a registration based approach to sensor network localization we consider a registration based approach for localizing sensor networks from range measurements this is based on the assumption that one can find overlapping cliques spanning the network that is for each sensor one can identify geometric neighbors for which all inter sensor ranges are known such cliques can be efficiently localized using multidimensional scaling however since each clique is localized in some local coordinate system we are required to register them in a global coordinate system in other words our approach is based on transforming the localization problem into a problem of registration in this context the main contributions are as follows first we describe an efficient method for partitioning the network into overlapping cliques second we study the problem of registering the localized cliques and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates in particular we present a method for efficiently testing rigidity and a proposal for augmenting the partitioned network to enforce rigidity a recently proposed semidefinite relaxation of global registration is used for registering the cliques we present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state of the art methods in terms of run time accuracy and scalability

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

saddlepoint approximations and tests based on multivariate m estimates we consider multidimensional m functional parameters defined by expectations of score functions associated with multivariate m estimators and tests for hypotheses concerning multidimensional smooth functions of these parameters we propose a test statistic suggested by the exponent in the saddlepoint approximation to the density of the function of the m estimates this statistic is analogous to the log likelihood ratio in the parametric case we show that this statistic is approximately distributed as a chi squared variate and obtain a lugannani rice style adjustment giving a relative error of order we propose an empirical exponential likelihood statistic and consider a test based on this statistic finally we present numerical results for three examples including one in robust regression

fast and accurate approximate double bootstrap confidence intervals we propose two new methods for the construction of approximate iterated bootstrap confidence intervals our methods follow a saddlepoint approach but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique the main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small to moderately sized samples and that they achieve this accuracy with very substantial reductions in computation time compared to other methods

tail probability approximations for student s t statistics in this paper we derive saddlepoint approximations for student s t statistics for strongly nonlattice random variables without moment conditions under very mild conditions we show that saddlepoint equations always have solutions

exact convergence rate and leading term in central limit theorem for student s t statistic the leading term in the normal approximation to the distribution of student s t statistic is derived in a general setting with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law the form of the leading term is shown to have its origin in the way in which extreme data influence properties of the studentized sum the leading term approximation is used to give the exact rate of convergence in the central limit theorem up to order n 1 2 where n denotes sample size it is proved that the exact rate uniformly on the whole real line is identical to the exact rate on sets of just three points moreover the exact rate is identical to that for the non studentized sum when the latter is normalized for scale using a truncated form of variance but when the corresponding truncated centering constant is omitted examples of characterizations of convergence rates are also given it is shown that in some instances their validity uniformly on the whole real line is equivalent to their validity on just two symmetric points

saddlepoint approximation for the distribution of a ratio of quadratic forms in normal variables abstract in this article the saddlepoint approximations to the density and tail probability of a ratio of quadratic forms in normal variables are derived a numerical exposition via the durbin watson test statistic reveals several desirable features the approximations which involve only a limited number of computable functions provide the practitioner with an accessible and a very powerful tool

self normalized cramer type large deviations for independent random variables let x 1 x 2 be independent random variables with zero means and finite variances it is well known that a finite exponential moment assumption is necessary for a cramer type large deviation result for the standardized partial sums in this paper we show that a cramer type large deviation theorem holds for self normalized sums only under a finite 2 th moment 0 1 in particular we show p s n v n x 1 x 1 o 1 1 x 2 d 2 n for 0 x d n where d n n i 1 ex 2 i 1 2 n i 1 e x i 2 1 2 and v n n i 1 x 2 i 1 2 applications to the studentized bootstrap and to the self normalized law of the iterated logarithm are discussed

double bootstrap methods that use a single double bootstrap simulation we show that when the double bootstrap is used to improve performance of bootstrap methods for bias correction techniques based on using a single double bootstrap sample for each single bootstrap sample can be particularly effective in particular they produce third order accuracy for much less computational expense than is required by conventional double bootstrap methods however this improved level of performance is not available for the single double bootstrap methods that have been suggested to construct confidence intervals or distribution estimators

analytical approximations to conditional distribution functions abstract conditional inference plays a central role in statistics but determination of relevant conditional distributions is often difficult we develop analytical procedures that are accurate and easy to apply for approximating conditional distribution functions for a continuous random vector we estimate conditional tail probabilities are smooth functions of x previous approaches have dealt with the cases where the variable whose conditional distribution is sought is a linear function of means and where there are p 1 conditioning variables however in many practical circumstances the statistic of interest is a nonlinear function of means and it is advantageous to condition on a lower dimensional ancillary statistic our procedure first involves approximating the marginal density function by an approach of phillips 1983 and tierney kass and kadane 1989 an accurate approximation to the required conditional probability is then obtained by applying a marginal tail probability approximation of diciccio and martin 1991 to the conditional density our method is illustrated in several examples including one which uses a saddlepoint approximation for the density of x and the method is applied for conditional bootstrap inference

successive and asymptotically efficient localization of sensor nodes in closed form accurate localization of nodes in a sensor network is a crucial step before the sensor network can be utilized for various applications this paper proposes a successive estimation method to self localize the sensor nodes using time of arrival toa measurements through the aid of a few anchor nodes whose positions are known a priori the successive nature of the proposed algorithm makes it attractive for distributed computation in a resource constrained environment the proposed technique uses subsets of toas to obtain coarse sensor node estimates depending on available computation and transmission resources the node positions are refined to improve their accuracies the solution of the proposed node localization algorithm is algebraic and closed form which simplifies computation and avoids possible local convergence or divergence problems as in the traditional iterative approaches a main benefit of the proposed algorithm is that although it is closed form and performs successive estimation of the node locations it is able to reach the cramer rao lower bound crlb accuracy under white gaussian measurement noise with sufficient snr this is confirmed by the theoretical analysis and corroborated by simulations

uncertainty relations in models of market microstructure abstract this paper presents a new interacting particle system and uses it as a spin model for financial market microstructure the asymptotic analysis of this stochastic process exhibits a lower bound to the contemporaneous measurement of price and trading volume under the invariant measure in the frozen phase of the supercritical regime

empirical edgeworth expansions for symmetric statistics in this paper the validity of a one term edgeworth expansion for studentized symmetric statistics is proved we propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency as a result we obtain the second order correctness of the empirical edgeworth expansion for a very general class of statistics including u statistics l statistics and smooth functions of the sample mean we illustrate the application of the bootstrap in the case of a u statistic of degree two

simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements we address the sensor network localization problem given noisy range measurements between pairs of nodes we approach the nonconvex maximum likelihood formulation via a known simple convex relaxation we exploit its favorable optimization properties to the full to obtain an approach that is completely distributed has a simple implementation at each node and capitalizes on an optimal gradient method to attain fast convergence we offer a parallel but also an asynchronous flavor both with theoretical convergence guarantees and iteration complexity analysis experimental results establish leading performance our algorithms top the accuracy of a comparable state of the art method by one order of magnitude using one order of magnitude fewer communications

strassen type law of the iterated logarithm for self normalized increments of sums abstract let x x n n 1 be a sequence of independent identically distributed random variables with e x 0 and assume that e x 2 i x x is slowly varying as x i e x is in the domain of attraction of the normal law in this paper it is shown that a strassen type functional law of the iterated logarithm holds for self normalized increments of sums of such random variables

edgeworth expansion of a function of sample means many important statistics can be written as functions of sample means of vector variables a fundamental contribution to the edgeworth expansion for functions of sample means was made by bhattacharya and ghosh in their work the crucial cramer c condition is assumed on the joint distribution of all the components of the vector variable however in many practical situations only one or a few of the components satisfy conditionally this condition while the rest do not such a case is referred to as satisfying the partial cramer c condition the purpose of this paper is to establish edgeworth expansions for functions of sample means when only the partial cramer c condition is satisfied

confidence intervals for the risk ratio under inverse sampling in this paper we investigate various confidence intervals for the risk ratio under inverse sampling also known as negative binomial sampling three existing confidence intervals namely the confidence intervals that are based on fieller s theorem the delta method and the f statistic are reviewed and three new confidence intervals namely the score likelihood ratio and saddlepoint approximation sa based confidence intervals are developed comparative studies among these confidence intervals through monte carlo simulations are evaluated in terms of their coverage probabilities and expected interval widths under different settings our simulation results suggest that the sa based confidence interval is generally more appealing we illustrate these confidence interval construction methods with real data sets from a drug comparison study and a congenital heart disease study

variance stabilization for a scalar parameter summary we present a variance stabilizing transformation for inference about a scalar parameter that is estimated by a function of a multivariate m estimator the transformation proposed is automatic computationally simple and can be applied quite generally though it is based on an intuitive notion and entirely empirical the transformation is shown to have an appropriate justification in providing variance stabilization when viewed from both parametric and nonparametric perspectives further the transformation repairs deficiencies of existing methods for variance stabilization the transformation proposed is illustrated in a range of examples and its effectiveness to yield confidence limits having low coverage error is demonstrated in a numerical example

on the effect of random norming on the rate of convergence in the central limit theorem it is shown that studentizing i e normalizing by the sample standard deviation rather than the population standard deviation can improve the rate of convergence in the central limit theorem this provides concise confirmation of one feature of the folklore that a studentized sum is in some sense more robust than a normed sum the case of infinite population standard deviation is also examined 1 introduction our purpose in this paper is to show that studentizing the operation of replacing a population standard deviation in a norming constant by its sample estimate can improve the rate of convergence in the central limit theorem thus we provide concise confirmation of one feature of the folklore that a studentized sum is in some sense more robust than a normed sum the reason is that large deviations of summands which are responsible for slow rates of convergence when ordinary norming constants are used cancel from the sample mean and sample standard deviation remark 3 7 in section 3 will give an intuitive explanation of the mechanism behind this cancellation note that the large deviations have a particularly subtle influence since under the condition that the distribution is attracted to the normal law the largest summand is negligible in comparison with the sum itself section 2 will briefly survey results on rates of convergence in the ordinary i e nonstudentized central limit theorem and will discuss their connection with our work section 3 will state our main results and summarize their consequences and section 4 will give proofs

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12