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线性秩统计量、有限总体抽样、置换检验与缩尾处理AI 解读

Asymptotic normality and a representation of all possible subsequential limiting distributions of a simple linear rank statistic are obtained. This is then applied to finite sampling and permutation tests for slope coefficients. The effects of Winsorizing in these situations are considered carefully. Of particular interest regarding slope coefficients is that either using normal score regression constants or Winsorizing slowly increasing numbers of the population values will…

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随机均值AI 解读

General theorems on asymptotic normality of randomly trimmed and Winsorized means are obtained. A new small sample studentization is proposed. Many examples are presented. The two sample problem is also considered.

非独立同分布情形下约化经验与分位数过程的收敛及其顺序统计量应用AI 解读

Any triangular array of row independent $\mathrm{rv}$'s having continuous $\mathrm{df}$'s can be transformed naturally so that the empirical and quantile processes of the resulting $\mathrm{rv}$'s are relatively compact. Moreover, convergence (to a necessarily normal process) takes place if and only if a simple covariance function converges pointwise. Using these results we derive the asymptotic normality of linear combinations of functions of order statistics of non-i.i.d. $\mathrm{rv}$…

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尺度参数比的检验与估计AI 解读

Let X 1, …, Xm and Y 1, …, Yn be independent random samples from populations having continuous d.f.'s Ψ((x-μ)/σ) and Ψ ((y-v)/τ) respectively. The classical F-test of a hypothesis concerning λ = τ/σ is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e. and Monte Carlo studies of power functions. An approximate permutation test [13] and a “jackknife” procedure [9] are found to be most satisfactory;…

尺度参数比的检验与估计AI 解读

Let X 1, …, Xm and Y 1, …, Yn be independent random samples from populations having continuous d.f.'s Ψ((x-μ)/σ) and Ψ ((y-v)/τ) respectively. The classical F-test of a hypothesis concerning λ = τ/σ is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e. and Monte Carlo studies of power functions. An approximate permutation test [13] and a “jackknife” procedure [9] are found to be most satisfactory;…