Properties of adaptively weighted Fisher's method

Using Weighted P-Values in Fisher's Method

Fisher's method prescribes a way to combine p-values from multiple experiments into a single p-value. However, the original method can only determine a combined p-value analytically if all constituent p-values are weighted equally. Here we present, with proof, a method to combine p-values with arbitrary weights.

Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables

We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.

The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions

This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be weighted in a predetermined way. The use of weighted estimates has a long history including applications to regression, rank statistics and Bayes theory. However, asymptotic results have generally been only first order (the CLT and weak convergence). We give third order asymptotics for the distribution and percentiles of any smooth functional of a weighted empir…

用于矩阵补全的自适应加权最近邻

Adaptively-weighted Nearest Neighbors for Matrix Completion

本文提出 AWNN 自适应加权最近邻矩阵补全方法，通过平衡偏差—方差权衡自动选择半径与权重，并在最少假设下给出理论保证及合成实验验证。

Asymptotic behaviour of weighted differential entropies in a Bayesian problem

We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density function conditional on $x$ successes after $n$ conditionally independent trials, when $n \to \infty$. It is shown that after an appropriate normalization in cases $x \sim n$ and $x$ $\sim n^β$ ($0<β<1$) limiting distribution is Gaussian and the differential entropy of standardized RV converges to differential entropy of standard Gaussian random variable. When $x$ …

对贝赫伦-费希尔问题的统一方法

A unified approach to the Behrens-Fisher problem

本文提出统一框架研究两样本贝赫伦-费希尔问题，推导出经典检验统计量的零分布表达式，通过梅林-巴恩斯因子分解将二维积分转化为单轮廓积分，揭示超几何结构的形成及尾部分析方法。