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使用 Bootstrap 构造分布函数置信带AI 解读

We first discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling but do not assume that F is continuous. The known alternative approach is to use the quantiles from the tabled Kolmogorov distribution. This approach is known to be conservative. It has already been shown in Bickel and Freedman (1981) that the bootstrap confidence band has the correct coverage probability asymptotically. We show by…

弱收敛与单点密度的有效估计AI 解读

We consider estimators for a multivariate probability density at a point. Efficient choices require knowledge of the density and its second derivatives although these are not known. We use consistent, but not necessarily efficient, estimators for these and use them to replace the unknown values in the choices for an efficient estimator. Our second stage estimators and the unattainable efficient choices are asymptotically equivalent. This follows because we show that an…