摘要:

The paper is mainly a survey of the topic how to approximate the probability density of the parameter estimator in a nonlinear regression model. A short presentation of the geometry of the model and a heuristic discussion of the model and a heuristic discussion of the “irregularities” of the estimates are given. In the model with Gaussian errors we present the asymptotic normal approximation, the approximationby the second order Edgeworth expansion, a conditional density of BARNDORFF-NIELSEN, and mainly the approximation called “flat” or “saddlepoint” approximation, which will be shown to have several interesting properties. Further, we present the possibility of improving the approximation in some models, the extension of the approximation to some cases of nongaussian errors, and besides the maximum likelihood estimator we consider also the weighted least-squares estimator, with the weights not depending on the error concariance matrix.

ISSN:0233-1888    

DOI:10.1080/02331889008802249

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

A simulation study has been carried out in order to compare different methods for calculating approximate confidence intervals for parameters in nonlinear regression, when the number of observations is small. We are particularly interested in methods for which it is possible to appreciate (asymptotically) the degree of approximation. In fact, two types of approach to the problem can be distinguished. The first one is based on the estimate's asymptotic law which can be calculated using Edgeworth expansions, the second one is based on resampling methods, such as bootstrap. For the different models considered in this simulation study, it appears that the first order asymptotic method gives the best result when the estimator is nearly normally distributed, the second order asymptotic must be used very cautiously, the bootstrap method gives quite good results for disturbed {biased and far from a Gaussian) estimators.

ISSN:0233-1888    

DOI:10.1080/02331889008802251

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

In the linear correlation model one observes an i.i.d. sequence (Xi, F$), i^l, of {p + l)-variate random vectors satisfying Yi=Xif}+ei. In this paper, we show the validity of the bootstrap for the LSE of p under minimal moment assumptions, answering a question posed by D. FREEDMAK

ISSN:0233-1888    

DOI:10.1080/02331889008802252

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

Least squares approximations are given for both the structural expectation and the unsampled population values in a finite population model with an auxiliary variable which is categorical. An ANOVA model is used as a guideline and a motivation. The linear BAYES approach is shown to provide an easy and operational solution to the well known difficulty of integrating out the superpopulation parameters in a BAYESian framework.

ISSN:0233-1888    

DOI:10.1080/02331889008802253

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

In order to obtain the first and second moments of a matrix quadratic form under normality assumptions its moment generating function will be derived and then differentiated.

ISSN:0233-1888    

DOI:10.1080/02331889008802254

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

M. Kläy, H. Riedwyl: ALSTAT 1. Algorithmen der Statistik für Kleinrechner. (Programm–Praxis, Bd. 1) 248 S., DM 44,–

ISSN:0233-1888    

DOI:10.1080/02331889008802255

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

This paper explores the rate at which the estimates of the unknown parameters in an autoregressive process converge in distribution to the normal variate.

ISSN:0233-1888    

DOI:10.1080/02331889008802256

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

For a multidimensional continuous time GAUssian process whose mean vector depends linearly of a multidimensional parameter, we consider a sequential estimation niodel. A suitable estimator process is constructed, and its distributions are analyzed in order to prove that it is progressively sufficient, After the reduction by sufficiency, an invariant structure is introduced and the optimal invariant terminal decision function is obtained.

ISSN:0233-1888    

DOI:10.1080/02331889008802257

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor

摘要:

H. Kunita: Lectures on stochastic flows and applications. Tata Institute of Fundamental Research, Bombay 1986. (Published by Springer–Verlag, Berlin – Heidelberg – New York – Tokyo 1986.), 126 pp., DM 20–

ISSN:0233-1888    

DOI:10.1080/02331889008802258

出版商:Akademie-Verlag    

年代:1990

数据来源: Taylor