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结合 Kendall 秩相关与符号检验的非参数线性回归检验AI 解读

A nonparametric test for hypotheses concerning linear regression parameters is based on the signs of the residuals and their Kendall correlation with the independent variable. The small-sample distribution of the test statistic is tabulated, asymptotic approximations are derived, and the corresponding confidence region is presented. Furthermore, the Pitman asymptotic relative efficiency of the test is calculated with respect to the classical test based on least squares and…

加性区组效应下完全区组分析中的加权排序AI 解读

The standard nonparametric procedures for testing the hypothesis of no treatment effects in a complete blocks experiment depend entirely on the within-block rankings. If block effects are assumed additive, however, then between-block information may be recovered by weighting these rankings according to their credibility with respect to treatment ordering. (For the special case of only two treatments, the sign test exemplifies use of unweighted rankings and the signed-rank…

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基于残差符号的回归分析AI 解读

Consider the regression model Y i = f(X i ) + E i, in which the errors are independent and have median 0. Then H 0: f ≡ h may be rejected for large values of , where S i = sgn(Y i — h(X i )) and γ ij = 1 or 0 according as X i and X j are in some sense “close” or not. The distribution of Q under H 0 can be obtained exactly by complete enumeration, or approximately using easily calculated moments; confidence regions for f or its parameters can be obtained by inverting the…

带截距回归曲面的单侧同时置信界AI 解读

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffé two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

含截距回归曲面的单侧同时置信界AI 解读

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffé two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

基于秩的协方差分析AI 解读

Various methods are discussed for the problem of comparing two or more populations with respect to a response variable Y in the presence of a (possibly multivariate) concomitant variable X—a situation in which the usual method is the standard one-way analysis of covariance. A method based on ranks is developed.