摘要:

We study the higher order correlation coefficients. These coefficients complement the classical correlation coefficient by measuring some dependences more and more sharply. We prove that they can detect the existence of functional dependence of typeg(X) =g′(Y). We obtain the asymptotic distribution of higher order empirical correlation coefficients. We deduce an Hilbertian Independence test.

ISSN:0233-1888    

DOI:10.1080/02331889308802427

出版商:Gordon and Breach Sceince Publishers    

年代:1993

数据来源: Taylor

摘要:

Results presented in previous authors papers are extended from the case of a low dimension of the parameter to the case of an arbitrary dimension. In particular, for arbitrary nonlinear regression models with normal errors, we present in an explicit form the “almost exact” density of the maximum likelihood estimator. It is a better approximation than the one obtained by the saddle-point method. In all obtained results the Riemannian curvature tensor is of great importance.

ISSN:0233-1888    

DOI:10.1080/02331889308802428

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

We consider the Bayesian optimal design problem in the usual linear regression model. A version of Elfving’s Theorem is proved for a model robust Bayesian c-optimality criterion. The optimal design minimizes a weighted product where the factors are proportional to the expected posterior risks of the Bayesian estimators for the linear combinations of the parameters in different models. The geometric characterizations are used to state sufficient conditions which guarantee that the classical and the Bayesian optimal designs are supported at the same set of points or are identical. The Bayesian D-optimal design problem appears as a special case in this setup considering “nested” models and special linear combinations for the paramater of the “highest coefficients” in different models. Thus sufficient conditions on the precision matrices of the prior distribution are found that the Bayesian D-optimal and the classical optimal design are supported at the same set of points or are identical. The results are illustrated in several examples.

ISSN:0233-1888    

DOI:10.1080/02331889308802429

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Ordinary or weighted jackknife variance or bias estimates may be very inefficient. We show this in thek-sample model, where their risks arektimes larger than for the estimates from asymptotic theory. We propose “extended jackknife estimates” intended to overcome this possible inefficiency. Indeed in thek-sample model they are identical to the “asymptotic” estimates which are also best unbiased and bootstrap estimators. This we show even for general linear models. Under a nonlinear regression model we get a high order asymptotic equivalence between extended jackknife and asymptotic estimates. A considerable small sample improvement over the ordinary or weighted jackknife may be expected, at least for models with a structure near to that of thek-sample problem.

ISSN:0233-1888    

DOI:10.1080/02331889308802430

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Some new methods of construction of rectangular designs which are 3-associate partially balanced incomplete block designs with a rectangular association scheme are presented. Such rectangular designs which may be new are tabulated under the range ofr,k≤ 10.

ISSN:0233-1888    

DOI:10.1080/02331889308802431

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

General classes of conjugate exponential family priors are identified for exponential family likelihoods. Both joint and conditional specification of the priors are discussed. The normal and inverse Gaussian cases provide illustrations.

ISSN:0233-1888    

DOI:10.1080/02331889308802432

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper we discuss some moment properties of a symmetric generalized logistic distribution indexed by a shape parameter λ and denoted by GL(λ, λ), and show that it is asymptotically normal as λ → ∞, and asymptotically double exponential as λ → 0. We also show that GL(λ, λ) can be used to approximate the normal distribution. The proposed approximation is illustrated for specific values of λ.

ISSN:0233-1888    

DOI:10.1080/02331889308802433

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Consul, P. C.; Generalized Poisson Distributions. Properties and Applications. (Statistics. textbooks and monographs; v. 99). Marcel Dekker, Inc., New York and Base1 i989, 320 pp.. $89.75 (CS. Canada); $107.50 (all other countries).

ISSN:0233-1888    

DOI:10.1080/02331889308802434

出版商:Gordon & Breach Science Publishers    

年代:1993

数据来源: Taylor

ISSN:0233-1888    

DOI:10.1080/02331889208802426

出版商:Gordon and Breach Sceince Publishers    

年代:1993

数据来源: Taylor