A note on breaking ties among sample medians

Efficient implementation of median bias reduction with applications to general regression models

In numerous regular statistical models, median bias reduction (Kenne Pagui et al., 2017) has proven to be a noteworthy improvement over maximum likelihood, alternative to mean bias reduction. The estimator is obtained as solution to a modified score equation ensuring smaller asymptotic median bias than the maximum likelihood estimator. This paper provides a simplified algebraic form of the adjustment term for general regular models. With the new formula, the estimation procedure benefits from a considerable computational gain by avoiding multiple summations and thus allows an efficient impleme…

Note on the robustification of the Student $t$-test statistic using the median and the median absolute deviation

In this note, we propose a robustified analogue of the conventional Student $t$-test statistic. The proposed statistic is easy to implement and thus practically useful. We also show that it is a pivotal quantity and converges to a standard normal distribution.

关于带结Steel检验的研究

On Steel's Test with Ties

本文重新研究带结情形下Steel多重比较检验，推导Wilcoxon统计量在条件随机化分布下的矩与渐近多元正态性，给出正态近似与单次数值积分方法，并在R包kSamples中实现，同时讨论扩展到所有两两比较。

LikelihoodGeometry：Macaulay2 软件包

LikelihoodGeometry: Macaulay2 Package

本文介绍了用于 Macaulay2 的 LikelihoodGeometry 软件包，它提供构建离散代数统计模型似然对应关系、组合模型及计算 ML-degree 的工具，将数据与极大似然估计联系起来。

基于C统计量精度的二分类预测模型外部验证中样本量估计的闭式解注记

A note on closed-form solutions for estimating sample size when externally validating a binary prediction model based on $C$-statistic precision

针对外部验证中C统计量精度所需的样本量估计，通过代数重排Newcombe公式得到七种闭式解，比迭代法快数十万倍且结果一致。

Finite-sample Rousseeuw-Croux scale estimators

The Rousseeuw-Croux $S_n$, $Q_n$ scale estimators and the median absolute deviation $\operatorname{MAD}_n$ can be used as consistent estimators for the standard deviation under normality. All of them are highly robust: the breakdown point of all three estimators is $50\%$. However, $S_n$ and $Q_n$ are much more efficient than\ $\operatorname{MAD}_n$: their asymptotic Gaussian efficiency values are $58\%$ and $82\%$ respectively compared to $37\%$ for\ $\operatorname{MAD}_n$. Although these values look impressive, they are only asymptotic values. The actual Gaussian efficiency of $S_n$ and $Q_n…