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大量独立检验中错误原假设比例的估计AI 解读

We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower 100(1−α)% confidence bounds for this proportion, based on the empirical distribution of the p-values of the tests. Methods in this family are then compared in terms of ability to consistently…

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天气与售电量关系的半参数估计AI 解读

A nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data. This accommodates introduction of covariates, timing adjustments due to the actual billing schedules, and serial correlation. The procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross-validation criterion introduced by…

非参数回归的带宽选择AI 解读

This paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression. We analyze a tapered Fourier series estimate and discuss the relationship of this estimate to a kernel estimate. We first consider a method based on an unbiased estimate of mean square error, and show that the bandwidth thus chosen is asymptotically optimal. Other methods are examined as well and are shown to be asymptotically equivalent. A small simulation shows,…

平滑样条：回归、导数与反卷积AI 解读

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel integral equation. These results are derived by developing a Fourier representation for a smoothing spline.

用B样条对微量荧光测定直方图进行反卷积AI 解读

We consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors. We propose a method of estimation using spline functions, discuss the numerical implementation of the method, and prove its consistency. The problem is motivated by the analysis of DNA content obtained by microfluorometry, and an example of such an analysis is included.

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