tensor notation and cumulants of polynomials a modified and extended tensor notation is introduced that is sufficient to cover multivariate moments and cumulants as special cases using this notation two basic identities are given the first of these expresses generalized cumulants in terms of ordinary cumulants the second gives the joint cumulant generating function of any polynomial transformation in terms of the cumulants of the original variables three applications of the basic identities are given the first application is concerned with sample cumulants or k statistics the second to edgeworth series and the third to exponential family models

high order asymptotic expansions for robust tests summary this paper provides high order asymptotic expansions for the m ratio and the signedroot m ratio robust test statistics which allow one to compute accurate approximations to significance or critical values using the edgeworth approximation the bartlett correction the variance correction or the saddlepoint approximation specific results are obtained for the linear regression model with the huber m estimator a monte carlo study illustrates the numerical accuracy of these approximations with respect to the usual first order approximations

on the number of positive solutions of weakly non linear elliptic equations when a parameter is large on etudie les solutions positives du probleme u f u dans u 0 sur ou est un domaine borne lisse de r n f r r est c 1 et est grand

two sample tests and one way manova for multivariate biomarker data with nondetects testing whether the mean vector of a multivariate set of biomarkers differs between several populations is an increasingly common problem in medical research biomarker data is often left censored because some measurements fall below the laboratory s detection limit we investigate how such censoring affects multivariate two sample and one way multivariate analysis of variance tests type i error rates power and robustness to increasing censoring are studied under both normality and non normality parametric tests are found to perform better than non parametric alternatives indicating that the current recommendations for analysis of censored multivariate data may have to be revised copyright 2016 john wiley sons ltd

exponential stability of numerical solutions for a class of stochastic age dependent capital system with poisson jumps recently numerical solutions of stochastic differential equations have received a great deal of attention numerical approximation schemes are invaluable tools for exploring their properties in this paper we introduce a class of stochastic age dependent vintage capital system with poisson jumps we also give the discrete approximate solution with an implicit euler scheme in time discretization using gronwall s lemma and barkholder davis gundy s inequality some criteria are obtained for the exponential stability of numerical solutions to the stochastic age dependent capital system with poisson jumps it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions where information on the order of approximation is provided these error bounds imply strong convergence as the timestep tends to zero a numerical example is used to illustrate the theoretical results

improved likelihood ratio statistics for exponential family nonlinear models summary this paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models corrected up to order n 1 where n is the sample size this result generalizes previous work by cordeiro 1983 various general bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed

uniqueness of positive solutions for a class of elliptic boundary value problems on demontre l unicite des solutions non negatives du probleme aux valeurs limites u f u pour x u 0 pour x ou 0 et est un domaine borne de r n a frontiere lisse

uniqueness of the solution of a semilinear boundary value problem on considere le probleme aux valeurs limites suivant 2 u f x u 0 x u x 0 x sur pour e 0 il y a un e 0 tel que pour 0 e e ce probleme ait une solution positive unique u dans c 2 c

on bartlett adjustments for approximate bayesian inference summary in wide generality the posterior distributions of the likelihood ratio statistic and the posterior ratio statistic are chi squared to error of order o n where n is sample size the error in the chi squared approximation can be reduced to order o n 2 by bartlett correction in this paper explicit formulae are derived for the bartlett adjustment factors of both statistics and the derivations are based on the tierney kass kadane 1989 asymptotic approximation for marginal posterior probability density functions the use of numerical differentiation to facilitate calculation of the bartlett adjustments is also described some applications are considered that concern inference about regression models from both complete and right censored data

coordinate systems and taylor series in statistics a geometric theory of taylor series is presented and shown to reduce to the choice of a set of coordinates at each point of a family of probability distributions the so called coordinate string any family admits a naturally defined coordinate string which generalizes the natural coordinates of exponential families this concept gives a coordinate free description of the mobius derivatives of mccullagh cox and the connection strings of barndorff nielsen

a uniqueness result for a singular nonlinear eigenvalue problem alfonso castrodepartment of mathematics harvey mudd college claremont ca 91711 usa castro math hmc edu eunkyung kodepartment of mathematics and statistics mississippi state university mississippi state ms 39762 usa ekko1115 gmail com r shivajidepartment of mathematics and statistics university of north carolinaat greensboro greensboro nc 27412 usa shivaji uncg edu

exponential stability of numerical solutions to sddes with markovian switching abstract the main aim of this paper is to investigate the exponential stability of the euler method for a class of autonomous stochastic delay differential equations with markovian switching the definition of exponential mean square stability of numerical method is introduced it is proved that the euler scheme is exponentially stable in mean square sense several examples are given for illustration

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

positive radial solutions to classes of singular problems on the exterior domain of a ball abstract we study positive radial solutions to singular boundary value problems of the form u k x f u u in u c u u 0 x r 0 u x 0 x where u div u is the laplacian operator of u x r n x r 0 0 n 2 0 k c r 0 0 is such that k s 1 s n for s 1 for some 1 min 1 n 2 and u is the outward normal derivative of u on x r 0 here f c 1 0 r is such that f s s 1 0 as s and c c 0 0 we analyse the cases when a f 0 0 and b f 0 0 we discuss existence non existence multiplicity and uniqueness results we prove our existence results by the method of sub and supersolutions

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

convergence of numerical solutions for a class of stochastic age dependent capital system with random jump magnitudes in stochastic differential equations sdes there is a class of stochastic functional differential equations with random jump magnitudes which aries in many financial models in general most equations of stochastic age dependent capital system do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties in this paper the numerical approximation is established for a class of stochastic age dependent capital system with random jump magnitudes the main aim of this paper is to investigate the convergence of the numerical approximation for a class of stochastic age dependent capital system with random jump magnitudes it is proved that the numerical approximate solutions converge to the analytical solutions of the equations under given conditions the numerical approximate results in zhang et al 2011 2 are improved an example is given for illustration

practical exponential stability of stochastic age dependent capital system with levy noise abstract it is well known that stability is one of most important topics in economy and control in this paper we focus on the practical stability problem for a class of stochastic age dependent vintage capital system with levy noise compared with the classical lyapunov stability theory practical stability can depict not only qualitative behavior but also quantitative properties such as specific trajectory bounds and specific transient behavior with the help of the stochastic analysis theory and ito s formula we establish some novel criteria for the mean square and almost sure practical exponential stability of the addressed system the obtained results improve some previous works given in the literature moreover an example is provided to illustrate the theoretical results

stability of solution to a class of investment system abstract the investment model of nonlinear stochastic neutral technical progress with time delay is given in this paper adopting the theory of stochastic functional differential equation and using ito formula gronwall s lemma and barkholder davis gundy s lemma exponential stability of strong solution is proved for the system of nonlinear stochastic neutral technical progress assets with time delay on hilbert space also a sufficient condition of the exponential stability is obtained the results are the improvement and extension of the existed results of this field

invariants and likelihood ratio statistics because the likelihood ratio statistic is invariant under reparameterization it is possible to make a large sample expansion of the statistic itself and of its expectation in terms of invariants in particular the bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log likelihood derivatives such expansions are given first for a scalar parameter and then for vector parameters geometrical interpretation is given where possible and some special cases discussed

accurate directional inference for vector parameters in linear exponential families we consider inference on a vector valued parameter of interest in a linear exponential family in the presence of a finite dimensional nuisance parameter based on higher order asymptotic theory for likelihood we propose a directional test whose p value is computed using one dimensional integration the work simplifies and develops earlier research on directional tests for continuous models and on higher order inference for discrete models and the examples include contingency tables and logistic regression examples and simulations illustrate the high accuracy of the method which we compare with the usual likelihood ratio test and with an adjusted version due to skovgaard in high dimensional settings such as covariance selection the approach works essentially perfectly whereas its competitors can fail catastrophically