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最小修剪差分回归估计量及其替代方法AI 解读

This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of…

最小截尾差分回归估计量及其替代方法AI 解读

This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of…

回归中最小可估子集近似的精度AI 解读

The elemental set algorithm involves performing many fits to a data set, each fit made to a subsample of size just large enough to estimate the parameters in the model. Elemental sets have been proposed as a computational device to approximate estimators in the areas of high breakdown regression and multivariate location/scale estimation, where exact optimization of the criterion function is computationally intractable. Although elemental set algorithms are used widely and…

《揭示多元异常值与杠杆点》：评论AI 解读

Detecting outliers in a multivariate point cloud is not trivial, especially when there are several outliers. The classical identification method does not always find them, because it is based on the sample mean and covariance matrix, which are themselves affected by the outliers. To avoid this masking effect, we propose to compute distances based on very robust estimates of location and covariance. In the case of regression data, the outliers also may be unmasked by using a…

异方差判别分析中的变量选择AI 解读

The likelihood ratio test statistic for the identity in means and covariance matrices of k normal populations has a well-known step-down decomposition measuring the contribution of each component of the vector observation. This decomposition in turn gives rise to three components testing the residual homo-scedasticity of each variable, the parallelism of its regression on its predecessors, and the identity of location. A variety of uses of this decomposition in selecting…

Professor A. M. Kshirsagar has pointed out that the un-numbered Lemma at the top of page 135 of Hawkins (1976) and the distributional result lower down in the page for the noncentral case are proved within the general context of canonical correlation in Kshirsagar (1972) pages 320 to 325.A special case is also to be found in Kshirsagar (1961).

观测序列位置参数突变的检验AI 解读

A possible alternative to the hypothesis that the sequence X 1, X 2, …, Xn are iid N(ξ, σ2) random variables is that at some unknown instant the expectation ξ shifts. The likelihood ratio test for the alternative of a location shift is studied and its distribution under the null hypothesis found. Tables of standard fractiles are given, along with asymptotic results.

多元方差分析中的变量子集选择问题AI 解读

Summary As with most other multivariate techniques, methods such as discriminant analysis which depend on multivariate analysis of variance are affected adversely by the inclusion of irrelevant variables. This paper discusses the problem of finding a parsimonious subset of variables that is essentially as good as the full set. As a result of the close computational similarity to multiple regression, a stepwise procedure, and a best subset method are derived from their…

利用主成分检测多元数据中的错误AI 解读

Serious problems arise in the maintenance of reliability in large data bases, since it becomes difficult to verify incoming data manually. This article considers the case in which the base consists of data vectors following a multivariate normal distribution. Five screening procedures are proposed—a “one-at-a-time” test, the standard χ2 test, and three statistics derived from principal component analysis. From analysis of a practical example, it emerges that the statistics…

次序统计量取值范围的界AI 解读

Let x1x2 ··· xn be any set of number satisfying Σ xi=0 Σ xi 2=1. There are bounds on the range of xi when the set {xi} is ranked (a) by x1≥x2≥ ··· ≥ xn and (b) by |x1|≥|x2|≥ ··· ≥|xn|. These bounds are given. The applicability to finite populotionr is pointed out.