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稳健与准稳健统计方法导论AI 解读

1. Introduction and Summary.- 1.1. History and main contributions.- 1.2. Why robust estimations?.- 1.3. Summary.- A The Theoretical Background.- 2. Sample spaces, distributions, estimators.- 2.1. Introduction.- 2.2. Example.- 2.3. Metrics for probability distributions.- 2.4. Estimators seen as functionals of distributions.- 3. Robustness, breakdown point and influence function.- 3.1. Definition of robustness.- 3.2. Definition of breakdown point.- 3.3. The influence…

摘要暂缺

稳健统计程序AI 解读

Background - Why Robust Procedures? Qualitative and Quantitative Robustness, Qualitative Robustness, Quantitative Robustness, Breakdown, Infinitesimal Robustness, Influence Function M-L and R-Estimates, L-Estimates, R-Estimates, Asymptotic Properties of M-Estimates, Asymptotically Efficient M-L, R-Estimates, Scaling Question Asymptotic Minimax Theory, Minimax Asymptotic Bias, Minimax Asymptotic Variance Multiparameter Problems, Generalities, Regression, Robust Covariances -…

使用稳健估计的广义线性与二次判别函数AI 解读

Two new methods of constructing robust linear and quadratic discriminant functions are introduced. The first is a generalization of Fisher's procedure for finding a linear discriminant function. It places less weight on those observations that are far from the overlapping regions of the two populations. The second new method substitutes M-estimates of the means and the covariance matrices into the usual expressions for the linear and quadratic discriminant functions. Monte…

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无分布假设的部分判别分析AI 解读

A distribution-free rank procedure is proposed for use in partial discrimination problems involving two populations. It is shown that this procedure can be applied with virtually any discriminant function. Moreover, the discriminant function may be selected after observing the samples on which it is to be based. Using Monte Carlo methods the rank procedure is compared with a normal theory and a tolerance region procedure. The rank procedure was the only one that adequately…

两样本自适应无分布检验AI 解读

An adaptive distribution-free test is proposed for the two-sample location problem. First, the data are used to assess the tailweight and skewness of the underlying distributions. This leads to the selection and then application, with the same data, of one of several common rank tests for shift, such as the Mann-Whitney-Wilcoxon test. The preliminary selection is made in a way that insures the testing procedure is distribution-free. A Monte Carlo study shows that the…

利用薪资数据估计百分位回归线AI 解读

In case of contamination, skewness or unequal variances, a nonparametric alternative to least squares regression is considered. In addition, investigators are often more interested in estimates of percentile lines than in the mean regression line. Thus, a modification of Brown-Mood regression is proposed to estimate the (100p) th percentile line α + βx of a random variable. This technique is applied to some data (artificial, but similar to real) relating the salary (y) of a…

自适应稳健程序：部分综述及应用与理论建议AI 解读

After providing some background for the need to consider estimates other than those resulting from normal theory, there is a brief review of some nonadaptive robust estimators. We introduce adaptive estimators using those of Tukey and McLaughlin, Jaeckel, Johns, Birnbaum and Miké, Takeuchi, Hàjek, van Eeden, and Beran. Adaptive estimators based on preliminary testing and Stein-like procedures are then considered, and recommendations are made on how to select the amount of…

底层分布的选择与自适应估计AI 解读

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the…

峰度及相关统计量的进一步分析AI 解读

We develop a scale invariant test for one member of the family given by the symmetric densities c exp [—|x|θ], θ>0 against another member. The statistic which arises in testing θ = 2 (normal) against θ = 4 is then modified to make it also location invariant; this modification results in the kurtosis K of the sample. Three other statistics are proposed for testing light-tailed distributions against heavy-tailed ones; in particular, the ratio V of one-half of the range and the…

若干不相关与独立的秩统计量AI 解读

Some interesting examples of uncorrelated simple linear rank statistics are listed. Consideration is then given to conditions under which general rank statistics are uncorrelated or have joint distributions which enjoy certain symmetric properties. Two simple linear rank statistics that are uncorrelated are found, under suitable restrictions, to be asymptotically independent. This is followed by some illustrations in which two rank statistics are exactly independent. The…

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统计假设的逐层分解AI 解读

Let ω0 be the space of a parameter θ. Let ω i be a subset of ω i–1, i = 1, 2, ···, k, We test θ∈ω k against θ∈ω0 – ω k by testing iteratively the following hypotheses: θ∈ωi against θ∈ω i–1 – ω i , i = 1, 2, ···, k. The hypothesis θ∈ω k is accepted if and only if all of the intermediate hypotheses are accepted. If the test statistic for each intermediate hypothesis is based on the corresponding likelihood ratio λ i , we demonstrate why, under fairly general conditions, these…