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多元密度椭球对称性的检验AI 解读

Let $Z$ be a random vector whose distribution is spherically symmetric about the origin. A random vector $X$ which is representable as the image of $Z$ under affine transformation is said to have an ellipsoidally symmetric distribution. The model of ellipsoidal symmetry is a useful generalization of multivariate normality. This paper proposes and studies some goodness-of-fit tests which have good asymptotic power over a broad spectrum of alternatives to ellipsoidal symmetry.

高效且稳健的自适应位置估计量AI 解读

A nonparametric minimum Hellinger distance estimator of location is introduced and shown to be asymptotically efficient at every symmetric density with finite Fisher information. Under small, possibly asymmetric, perturbations in such a density, the estimator is asymptotically robust in a technical sense which extends Hajek's concept of "regularity." A numerical example illustrates the computational feasibility of the estimator and its resistance to an arbitrary single…

参数模型的最小 Hellinger 距离估计AI 解读

This paper defines and studies for independent identically distributed observations a new parametric estimation procedure which is asymptotically efficient under a specified regular parametric family of densities and is minimax robust in a small Hellinger metric neighborhood of the given family. Associated with the estimator is a goodness-of-fit statistic which assesses the adequacy of the chosen parametric model. The fitting of a normal location-scale model by the new…

稳健位置估计AI 解读

Measures of location differentiable at every density in the Hellinger metric are constructed in this paper. Differentiability entitles these location functionals to the label "robust," even though their influence curves need not be bounded and continuous. The latter properties are, in fact, associated with functionals differentiable in the Prokhorov metric. A Hellinger metric concept of minimax robustness of a location measure at a density shape $f$ is developed.…

分布函数估计AI 解读

It is shown that the limiting distribution of any regular estimator of a continuous cdf on [0, 1] can be represented as a convolution of the Brownian bridge process with another distribution on $C\lbrack 0, 1\rbrack$. The result is related to Hajek's representation for limiting distributions of regular parametric estimators.

非中心二次型的尾概率AI 解读

Let $S(b) = \Sigma r\sigma r^2Xr^2(nr,br^2)$ be a positive linear combination of independent noncentral chi-square random variables. This note derives two representations for the tail probabilities P[S(b) >x], a Taylor series in the noncentrality parameters and a limiting form of this series for large x. An application of the latter result to statistical tests of Cramer-von Mises type is discussed.

趋势二次秩检验的局部渐近功效AI 解读

A general class of quadratic rank tests for randomness versus trend is introduced and studied in this paper. Included within this class are the Cramer-von Mises two sample test, the Watson two-sample test, and their extensions to trend alternatives. Analytical study is made of the asymptotic power and efficiency of such tests in a neighborhood of the null hypothesis.

位置模型中渐近有效的自适应秩估计AI 解读

This paper describes a new construction of uniformly asymptotically efficient rank estimates in the one and two-sample location models. The method adopted differs from van Eeden's (1970) earlier construction in three respects. First, the whole sample, rather than a vanishingly small fraction of the sample, is used in estimating the efficient score function. Secondly, a Fourier series estimator is used for the score function rather than a window estimator. Thirdly, the…