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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…

卡方拟合优度检验的功效近似：简单假设情形AI 解读

The limiting distribution of the chi-square goodness-of-fit statistic Tn under alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate as n → ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn − μ n )/σ n is standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two…

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…

Watson分布的均值与方差AI 解读

Summary Watson's distribution is the distribution of the ratio of two linear combinations of independent x22 variables (the denominator being positive). Such ratios arise, for example, in the consideration of, or in approximations to, certain serial correlation coefficients. The moments of these ratios are known only in specialized cases. We derive the first two moments for the more general Watson distribution.