摘要:

We consider the problem of estimating the unknown variance function υ in a nonparametric regression model. As a basis for our estimators we take estimated residuals which are based on a kernel estimator of the mean vector. Then we form with these residuals a kernel estimator of υ. Main emphasis is on a data-driven choice of the bandwidths involved in the procedure. It is shown that the risk of this estimator attains the uniform convergence rate in Sobolev classes for υ under weak smoothness assumptions on the mean. Moreover, we prove that there is asymptotically no loss due to the estimation of the mean.

ISSN:0233-1888    

DOI:10.1080/02331889408802445

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In the paper a new class of tests for variance components in two variance components model is presented. The tests are based on nonnegative admissible invariant quadratic estimators of variance components. A comparison of the tests with the known ones are given. Two-way classification models corresponding to block designs are considered separately. Examples of these models are given, for which the power functions of the tests are computed by using Imhof’s procedure, and compared with the attainable upper bound obtained by using the Neyman–Pearson Lemma.

ISSN:0233-1888    

DOI:10.1080/02331889408802446

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

summary.In Bonneu (1988) a prediction criterion for model selection is defined for Generalized Linear Models (GLM). This criterion, similar to AIC (Akaike, H. (1973)), Sakamoto, Y. and Akaike, H. (1978)) is based on the expected Kullback-Leibler discrepancy (Kullback, S. 1959)), especially defined for prediction. The model selection strategy is employed to select a Nelder's link function (1972) and a small subset of explanatory variables. Data are observed from an experimental design with unequal numbers of replications. This paper deals with the asymptotic estimate of this prediction criterion and compares it with a simulated bootstrap estimate. Usually asymptotic criteria for model selection can be written as the sum of a statistic and a bias (see Linhart, H. and Volkers, P. (1984); Linhart, H. and Zucchini, W. (1986)). In the present paper, asymptotic arguments are investigated in a different way, taking into account the prediction objective and GLM framework with unequal numbers of replicates.

ISSN:0233-1888    

DOI:10.1080/02331889408802447

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The problem of component wise estimation of ordered location parametersθ1(θ1≤θ2) of two independent exponential distributions is investigated. The scale parameters are assumed to be unequal but known. Independent random samples of unequal sample sizes are drawn from two populations and the estimators admissible among the mixed estimators ofθ1andθ2are obtained. It is shown that the minimum risk estimators (MREs) ofθ1andθ2without assumingθ1≤θ2are inadmissible when one does assume thatθ1≤θ2. The efficiencies of mixed estimators relative to MREs (without assumingθ1≤θ2) are tabulated for equal sample sizes and equal scale parameters.

ISSN:0233-1888    

DOI:10.1080/02331889408802448

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Motivated by circle fitting to spatial distributions, this paper looks at the relationship between the expected distance function and the radial density. Inversion of this relationship is given simply in dimensions 1 and 3 and generally by using Mellin transforms. Examples of variance function behaviour are given and calculations of the coefficient of sphericity shown.

ISSN:0233-1888    

DOI:10.1080/02331889408802449

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Three examples of point processes are given where the autocovariance decays in an inverse power law, but which are not fractal.

ISSN:0233-1888    

DOI:10.1080/02331889408802450

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

It is shown that the number of non-void arrangementsof {1, …k}, whereis some realization of a random variableXwith distributiondefined by,which occur in connection with the rencontre problem (as the probability formfixed points of permutations of {1, … ,n} selected with probability), is the uniquely determined unbiased estimator of. Herestands for the one-point mass at zero. Furthermore, the class of all unbiased estimators ofnwith respect to the family, where the casen= 0 is excluded, is determined and all locally MVU estimators at everyin the modelare characterized. In particular, it turns out that there does not exist a uniformly MVU resp. a locally MVU estimator fornat everyin the model.

ISSN:0233-1888    

DOI:10.1080/02331889408802451

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

STATGRAPHICS PLUS Version 5.2. STSC, Inc., Rockville, Maryland, U.S.A. and STSC, Europe, Windsor, England, 1991.

ISSN:0233-1888    

DOI:10.1080/02331889408802452

出版商:Gordon & Breach Science Publishers    

年代:1994

数据来源: Taylor

ISSN:0233-1888    

DOI:10.1080/02331889408802444

出版商:Gordon & Breach Sceince Publishers    

年代:1994

数据来源: Taylor