摘要:

Summary, This paper deals with the asymptotic behaviour of the (quasi-)maximum likelihood estimator in misspecified generalized linear models. Misspecification may be due to incorrect densities, wrong link functions, omitted regressors etc. It is shown that (quasi-Consistency and asymptotic normality can be obtained under conditions which permit substantial heterogeneity of the observations, The results are based on a general theorem on asymptotic inference under misspecification for i.n.i.d. observations, using full matrix normalization and avoiding domination or convergence conditions. For important subclasses of generalized linear models, admissible heterogeneity is characterized more explicitly in terms of the regressors

ISSN:0233-1888    

DOI:10.1080/02331889008802259

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

We consider the multivariate linear modelwhere Yiis a p-vector random variable, Xiis a q X p matrix, βÀ0is an unknown q-vector parameter and {si} is a sequence of iid p-vector random variable with median vector zero. The estimate βÀnof βÀ0such thatis called the least distances (LD) estimator. It may be recalled that the least squares (LS) estimator is obtained by minimizing the sum of norm squares. In this paper, it is shown that the LD estimator is unique, consistent and has an asymptotic q-variate normal distribution with mean β0and co variance matrix V which depends on the distribution of the error vectors {εi}. A consistent estimator of V is proposed which together with βÀnenables an asymptotic inference on β0. In particular, tests of linear hypotheses on β0analogous to those of analysis of variance in the GATJSS-MARKOFF linear model are developed. Explicit expressions are obtained in some cases for the asymptotic relative efficiency of the LD compared to the LS estimator.

ISSN:0233-1888    

DOI:10.1080/02331889008802260

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

ISSN:0233-1888    

DOI:10.1080/02331889008802261

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

The aim of the paper is to develop a linear estimation theory for the parameter in a linear regression model if random fuzzy-set-valued observations are available. There¬fore fuzzy sets and their basic (linear) operations and random fuzzy sets, especially their expectation and variance, are introduced and applied to random fuzzy numbers which are used to model vague observations. For a well-defined linear regression model the BLUE is characterized which only in special cases coincides approximately with the so-called extended least squares estimator

ISSN:0233-1888    

DOI:10.1080/02331889008802262

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

A.J. Dobson: An Introductin to Statistical Modelling. Champman and Hall, London 1986, paperback, 125 pp

ISSN:0233-1888    

DOI:10.1080/02331889008802263

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

An extension of the Theory of Polynomial Smoothing Splines is developed for the statistical problem of estimating a curve based on incomplete and noisy observations. The smoothness of a curve is measured by a quadratic function of its FOURIER transform in the space of tempered distributions. These splines, called a-splines, bring a new con¬nection between Smoothing Splines estimates and Kriging estimates: for the Polynomial Generalized Co variance, the Kriging estimate is equivalent to a particular a-spline

ISSN:0233-1888    

DOI:10.1080/02331889008802264

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

. Some quadratic tests of fit related to NEYMAN'S smooth tests as well as to a class of quadratic tests of fit introduced recently by NETTHATJS (1988) are considered. Attention is focused on the case of completely specified null distribution. The case when the number of summands in the test statistics goes to infinity is discussed. In this case, asymptotic distribution under the null hypothesis as well as under some sequences of alternatives are derived by means of the KOML6S, MAJOR and TTTSNADY embedding. Using the same technique, the asymptotic distribution of the classical ehi-square test is investigated in case when the number of cells tends to infinity

ISSN:0233-1888    

DOI:10.1080/02331889008802265

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

For square contingency tables with ordered categories, TOMIZAWA (1987) de¬composed the conditional symmetry (CS) model into two certain models. The purpose of this note is to point out that AKAIKE'S (1974) information criterion ignored a common constant for the CS model is equal to the sum of the criterions for the decomposed two models

ISSN:0233-1888    

DOI:10.1080/02331889008802266

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

F.C. Drost: Asymptotics for generalized chi–square goodness–of–fit tests. CWI Tract. 48, Mathematisch Centrum, Amsterdam 1988, 104 pp., Dfl. 16.30

ISSN:0233-1888    

DOI:10.1080/02331889008802267

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

The likelihood function is modified substituting the empirical distribution by a kernel estimator. The parametric estimate that is deduced by maximizing the modified likelihood has only a bias of order o(l/n) under certain conditions. Thus the bias of Maxi¬mum Likelihood Estimates is reduced. A modified version of the Maximum Likelihood Estimator of the shape parameter of the Weibuii distribution is studied as well for un-censored samples as for censored ones

ISSN:0233-1888    

DOI:10.1080/02331889008802268

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor