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81.
Frank Caridi 《Journal of multivariate analysis》1983,13(1):52-66
For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes. 相似文献
82.
In the first part of this paper we study the convergence of finite difference methods to approximate the maximal solution of problems of the form:u+f (x, u)=0, with boundary conditions eitheru(0)=u(b)=0 oru(0)=u (b)=0, 0<b1. The functionf(x, u) satisfies several conditions that are explicitly given in § 1. This work extends earlier results of Parter (see references at the end).Since this problem has in general more than one solution we develop in the second part two algorithms to approximate solutions characterized by the number of their zeros in (0, 1). We include in the last Section numerical results and some additional comments on the implementation of the algorithms on a digital computer.The research of this author was supported by the Office of Naval Research under contract No N-0014-67-A-0128-004.Part of this research was carried on while this author was visiting the Mathematics Research Center, University of Wisconsin, during the summer of 1969. 相似文献
83.
Paul Deheuvels 《Journal of multivariate analysis》1983,13(2):257-272
A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models. 相似文献
84.
M.A. Chmielewski 《Journal of multivariate analysis》1980,10(3):343-350
The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian m-vectors. In this paper this assumption is weakened by considering a class of distributions for which the vector observations are not necessarily either Gaussian or independent. This class contains the elliptically symmetric laws with densities of the form f(X(n × m)) = ψ[tr(X ? M)′ (X ? M)Σ?1]. For testing the equality of k scale matrices and for the sphericity hypothesis it is shown, by using the structure of the underlying distribution rather than any specific form of the density, that the usual invariant normal-theory tests are exactly robust, for both the null and non-null cases, under this wider class. 相似文献
85.
Peter Hall 《Journal of multivariate analysis》1983,13(2):234-256
Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation. 相似文献
86.
A tolerance region is a map from the sample space of one statistical model to the event space of a second statistical model having the same parameter. This paper derives an optimum β-expectation tolerance region for the multivariate regression model. A measure of power is proposed and evaluated. 相似文献
87.
For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented. 相似文献
88.
Michael D. Perlman 《Journal of multivariate analysis》1974,4(1):22-30
It is shown that for the MANOVA problem the power function of the test based on the trace of a multivariate beta matrix is monotonically increasing in each noncentrality parameter provided that the cutoff point is not too large. This result is also true for the problem of testing independence of two sets of variates. 相似文献
89.
The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors. 相似文献
90.
Summary Exact robustness studies against non-normality have been carried out for test of independence based on the four multivariate
criteria: Hotelling's trace,U
(p)
, Pillai's trace,V
(p)
, Wilks' criterion,W
(p)
, and Roy's largest root,L
(p)
. The density functions ofU
(p)
,W
(p)
andL
(p)
have been obtained in the canonical correlation case and further the moments ofU
(p)
and m.g.f. ofV
(p)
have been derived. All of the study is based on Pillai's distribution of the characteristic roots under violations. Numerical
results for the power function have been tabulated for the two-roots case. Slight non-normality does not affect the independence
test seriously.V
(2) is found to be most robust against nonnormality.
Yu-Sheng Hsu is now with Georgia State University, Atlanta. 相似文献