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再生核希尔伯特空间在函数型分类中的应用AI 解读

The Hájek–Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon–Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite-dimensional Gaussian measures, there are nontrivial examples of both situations when dealing with Gaussian stochastic processes. This article provides: (a) Explicit expressions for the optimal (Bayes)…

基于 L 统计量的二阶随机占优检验AI 解读

We use some characterizations of convex and concave-type orders to define discrepancy measures useful in two testing problems involving stochastic dominance assumptions. The results are connected with the mean value of the order statistics and have a clear economic interpretation in terms of the expected cumulative resources of the poorest (or richest) in random samples. Our approach mainly consists of comparing the estimated means in ordered samples of the involved…

回归 MM 估计与约束 M 估计的最大偏差函数AI 解读

We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the τ-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is,…