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混合随机过程经验累积分布函数的渐近分布理论AI 解读

This paper introduces a new mixing condition for stationary processes which is weaker than $\phi$-mixing but stronger than strong mixing. Many processes arising in applications, e.g., first order autoregressive processes, obey the conditions. The main result is that the empiric cdf of a sample from such processes converges to a Gaussian process.

利用分组数据界定分布矩AI 解读

This article derives bounds on a wide class of moments of the underlying distribution from data grouped in intervals when the mean of each group is given. The extremal distributions are constructed yielding the upper and lower bounds to moments of the form ∫h(x)dF(x), where h(x) is convex and F(x) is concave. To illustrate the results, bounds on the variance and Gini index are presented for two theoretical distributions.

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关于对称性的符号检验AI 解读

This article studies the effect of estimating the center of symmetry by the sample mean on the sign test for symmetry. Under the null hypothesis, the modified sign test is not distribution-free. Indeed, the asymptotic variance of the modified sign test can be quite different from that of the standard sign test.

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一类秩检验的渐近相对效率AI 解读

Summary A partial ordering is introduced in a class of rank tests according to the weight or emphasis they place on the middle ranks versus the extreme ones. This notion of order is shown to be related to van Zwet's partial ordering of symmetric densities according to the probability in their tails. Bounds on Pitman's asymptotic relative efficiency (a.r.e.) of several tests to the Wilcoxon test are established. Finally, a sharp lower bound for the asymptotic power of the…

论稳健统计程序AI 解读

This paper discusses a procedure for finding robust estimators of the location parameter of symmetric unimodal distributions. The estimators are based on robust rank tests and the methods used are applicable to other one parameter problems. To every density function there corresponds an asymptotically most powerful rank test (a.m.p.r.t.). For a set , of density functions the maximin rank test, R, maximizes the minimum limiting Pitman's efficiency of R relative to the…

两样本秩检验的百分位修正AI 解读

This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p th and bottom r th fractions of the combined sample. The percentile modified tests for scale are quite effective. When p = r = 1/8 (i.e., we score only the…