摘要:

For the usual quadratic risk, the minimax linear estimator, MILE, of a centred ellipsoid is always an admissible linear estimator, ALE. The main result of the paper is a characterization of the set of centred ellipsoids for which a given ALE, is also the MILE. The result is applied to found the MILE for centred ellipses of R2. Also, some light on the problem of finding the MILE of a centred ellipsoid is shed.

ISSN:0233-1888    

DOI:10.1080/02331888308802395

出版商:Gordon and Breach Science Publishers S. A.    

年代:1993

数据来源: Taylor

摘要:

Nonlinear regression models are used in many fields. Often the regression for observation-covariate pairs (X(ti), ti) is modeled as X(ti) =f(ti) + [d](fi), i = 1,. .. , n, where f is the continuous possible nonlinear mean function, while the ([d](ti))i=1.....nare zero mean, i.i.d. random errors having finite variance [d]2. The least squares methods for estimation of f are usually based upon a given parametric form of f. In this article we develop two statistical tests, one for testing that f belongs to a given class of functions possibly discontinuous in their first derivative, and another one for comparing two such classes. This is done by introducing an appropriate estimate of the unknown variance [d]2. The numerical results of a simulation study seem satisfactory.

ISSN:0233-1888    

DOI:10.1080/02331888308802396

出版商:1993 Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

Summary. Let Tnbe an M-estimator of a parameter [d], generated by a function [d]. It is shown under some conditions on [d] and the model {F[d]}[d]=[d] that the formula [d]n(Tn- [d]n+ (yn)-1[d]i=ni=n[d] (x, [d]n))= OG[d]nn(n-1/2holds for Gnand [d]nfrom an infinitesimal neighbourhood of F[d] and [d] respectively, for a constant y = y([d], F[d]). It is aiso considered a one-step version M(1)nof Tnsuch that, under the same conditions, Tn- M(1)n= OG[d]nn(n-1for every n1/2strong consistent initial estimator

ISSN:0233-1888    

DOI:10.1080/02331888308802397

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

Let X be a real random variable, [d], a parametric family of probability density functions, with parameter [d], of same support as X and a partition of this support into a fixed number of intervals. The aim of this paper is to test that the distribution of X belongs to [d] when a random sampie of n independent observations has been drawn but only the frequency and empirical mean of observations falling in each cell are available. For this kind of data, the estimation of [d] based on the Generalized Moments method straight forwardly leads to Chi-Square tests but computations are cumbersome. For that reason, simpler though non optimal estimators are often prefered. We examine both choices and discuss three examples:the Exponential, Cauchy and Normal Distributions.

ISSN:0233-1888    

DOI:10.1080/02331888308802398

出版商:1993 Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

Blumenthal and Cohen (1968c) and Dhariyal, Sharma and Krishnamoorthy (1985) considered the question of the existence of unbiased estimators of the larger (smaller) of the two parameters. In this paper, we first show the non-existence of such an unbiased estimator in case of two double exponential populations with unknown locations. We also give a general inadmissibility result and apply it to the uniform distribution

ISSN:0233-1888    

DOI:10.1080/02331888308802399

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

An estimation procedure is proposed for frequencies of a stationary random process in the case that the observation points form a Poisson point process. Using results of Chen and Masry it is proved that the estimators are consistent.

ISSN:0233-1888    

DOI:10.1080/02331888308802400

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

A major gene on a quantitative trait is supposed to have an additive effect in a linear model with fixed or random father effects. For a population of n families of m half sib each, the likelihood is that of a distribution mixture. The problem is to detect a major gene, by a test of the population homogeneity. We first review the identifiabiiity problems and study the asymptotic behaviour of the maximum likelihood test for a mixture of two distributions. Using the same notions, we study the asymptotic behaviour of the maximum likelihood test in the fixed father effects model, as n and m tend to infinity. Then, in the gaussian case, several approximations of the random father effects model are studied.

ISSN:0233-1888    

DOI:10.1080/02331888308802401

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

The bounds for the expected values of order statistics and their linear functions are obtained under the assumption that the exact value of the expectation of extreme order statistic is known for two smaller sample sizes. It is shown that the existing bounds can be improved considerably by making use of this information.

ISSN:0233-1888    

DOI:10.1080/02331888308802402

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

Summary. Relations between the univariate gamma, multivariate Dirichlet and Liouville distributions are investigated.

ISSN:0233-1888    

DOI:10.1080/02331888308802403

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor

摘要:

Summary. A counterexample to a statement that an obliquely reflected Brownian Motion can be used to construct a solution to the martingale problem for the Laplacian in an infinite two-dimensional

ISSN:0233-1888    

DOI:10.1080/02331888308802404

出版商:Gordon and Breach Science Publishers S.A.    

年代:1993

数据来源: Taylor