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约束M估计与回降型M估计的正则性和唯一性AI 解读

Constrained M-estimates of multivariate location and scatter are found by finding the global minimum of an objective function subject to a constraint. They are related to redescending M-estimates of multivariate location and scatter since any stationary point of the objective function corresponds to such an M-estimate. Unfortunately, even for the population form of the estimator, that is, the constrained M-functional, the objective function may have multiple stationary…

Procrustes 估计量的一致性AI 解读

Summary Lele has shown that the Procrustes estimator of form is inconsistent and raised the question about the consistency of the Procrustes estimator of shape. In this paper the consistency of estimators of form and shape is studied under various assumptions. In particular, it is shown that the Procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed. The…

复 Bingham 分布与形状分析AI 解读

SUMMARY A complex version of the Bingham distribution is defined on the unit complex sphere in Ck. Various statistical properties, including asymptotic normality under high concentration, are derived. Symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions. Strengths and weaknesses of this approach are investigated. Links and contrasts with Bookstein co-ordinates are discussed. A hybrid approach to principal…

删失生存数据的依赖性度量AI 解读

In the linear regression model with normal errors the squared product-moment correlation provides the standard measure of dependence between the explanatory variable and the response variable. Using the concept of information gain, a measure of dependence can also be defined for more general regression models used in survival analysis, such as the Weibull regression model or Cox's proportional hazards model. Further, this measure of dependence can be conveniently estimated…

非嵌套假设检验的内在结构AI 解读

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is…

非嵌套假设检验的内在结构AI 解读

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is…

方向数据有限混合模型的可识别性AI 解读

In some problems of directional data, finite mixtures of simple distributions have been proposed as statistical models. In this paper we show that for a wide class of directional distributions, all such mixtures are identifiable.

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似然比检验的稳健性质AI 解读

The usual asymptotic chi-squared distribution for the likelihood ratio test statistic is based on the assumptions that the data come from the parametric model under consideration and that the parameter satisfies the null hypothesis. In this paper we examine the distribution of the likelihood ratio statistic when the data do not come from the parametric model, but when the ‘nearest’ member of the parametric family still satisfies the null hypothesis. In general, the…