摘要:

This In memoriam is divided into three parts. The first part is a tribute to Albert Verbeek as a person and a scientist. In the second part, a short note is reproduced, translated from the Dutch, as an example how he applied himself to all kinds of problems. The final part consists of an overview of his major publications.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01331.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The main purpose of this paper is to unify and extend the existing theory of ‘estimated zeroes’ in log‐linear and logit models. To this end it is shown that every generalized linear model (GLM) can be embedded in a larger model with a compact parameter space and a continuous likelihood (a ‘CGLM’). Clearly in a CGLM the maximum likelihood estimate (MLE) always exists, easing a major data analysis problem. In the mean‐value parametrization, the construction of the CGLM is remarkably simple; except in a rather pathological and rare case, the estimated expected values are always finite., In the β‐parametrization however, the compactification is more complex; the MLE need not correspond with a finite β, as is well known for estimated zeros in log‐linear models. The boundary distributions of CGLMs are classified in four categories: ‘Inadmissible’, ‘degenerate’, ‘Chentsov’, and ‘constrained’. For a large class of GLMs, including all GLMs with canonical link functions and probit models, the MLE in the corresponding CGLM exists and is unique. Even stronger, the likelihood has no other local maxima. We give equivalent algebraic and geometric conditions (in the vein of Haberman (1974, 1977) and Albert and Anderson (1984) respectively), necessary for the existence of the MLE in the GLM corresponding to a finite β. For a large class of GLMs these conditions are also sufficient. Even for log‐linear

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01332.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The dynamic clustering (DC) algorithm is a method for discovering clusters in a given population. Unfortunately the classical DC algorithms fail to perform well in the presence of outliers. A robust dynamic clustering (RDC) algorithm is introduced to overcome this problem. Robust estimates of the location vector and the covariance matrix are calculated in the affine invariant case. A simulation study is presented to demonstrate the basic difference between the DC and the RDC algorithms. Three kinds of optimization criteria are used in case of contaminated multivariate normal distributions.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01333.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Some distributional results are derived for subset selection from logistic populations, differing only in their location parameter. The probability of correct selection is given. Exact and numerical results concerning the expected subset size are presented.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01334.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Asymptotic normality of M‐ or maximum likelihood type estimators was established in a classic paper by Huber (1967). Reeds (1976) argued that this could have been obtained simply as an application of the delta‐method, using the tool of compactly differentiating von Mises functionals with respect to the empirical distribution function Fn. His proof however contains some errors and has been largely ignored. A corrected version of the proof is gi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01335.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The celebrated local asymptotic minimax (LAM) theorem due to HÁjek (1972) also includes the statement that a LAM estimator Is necessarily asymptotically linear. A similar result. is true for semi‐parametric models, but Hájek's result doesn't apply to this case as the efficient influence function is often not contained in the (proper) tangent space. This note gives a simple, elementary proof of both the LAM theorem and the necessity of asymptotic linearity of a LAM estimator seque

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01336.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Often the usefulness of a random variate generator for a distribution is based on the successful generation of independent variates from the uniform distribution. However, no pseudo‐random number generator is capable of generating a truly random uniform sequence. As the cost of computations is now dramatically reduced, the computational efficiency should not be the primary criterion in choosing a good generator. Proposed here is a robustness criterion which is designed to study the effect of an imperfect pseudo‐random number generator on the accuracy of a random variate generator. In particular, the beta and binomial variate generators are examined for their robustness to the non‐uniformity of a pseudo‐random number ge

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01337.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

This pape; is concerned with distributional solutions of X1+…+ Xmd= U(X1+…+ Xm+n) where the X's are iid and independent ofUwhich takes values in [0,1]. WhenUis a constant the only possible non‐trivial solutions lie in the class of semi‐stable laws, and they are stable under a simple regularity condition. This material is reviewed. A unified account is given of some results known for the case whereUhas a beta (α, 1) law, apparently the only other case allowing explicit identification of all possible s

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01338.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01339.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1992.tb01340.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY