Posts on Andrey Akinshin

Previously, I have discussed how to build weighted versions of various statistical methods.

Multimodality of distributions is a severe issue in statistical analysis.

This post examines the pitfalls of naively replacing the mean with the median.

Normal or approximately normal subjects are less useful objects of research than their pathological counterparts.1 In the realm of software development, reliability is crucial.

In the previous post, we showed how the Edgeworth expansion can improve the accuracy of obtained p-values in the Mann-Whitney U test.

In previous posts, I have shown a severe drawback of the classic Normal approximation for the Mann-Whitney U test: under certain conditions, can lead to quite substantial p-value errors, distorting the significance level of the test.

In this post, we discuss the classic implementation of the Mann-Whitney U test for cases in which the considered samples contain tied values.

This post calculates the efficiency of the median, Hodges–Lehmann estimator, and midrange under the uniform distribution.

This post uncovers subtle problems in R’s built-in implementation of the Hodges–Lehmann estimator that can produce unexpected results.

In the previous post, I have discussed a huge difference between p-values evaluated via the R implementation of the Mann-Whitney U test between the exact and asymptotic implementations.

The Mann–Whitney U test (also known as the Wilcoxon rank-sum test) is one of the most popular nonparametric statistical tests.

I have just published a preprint of a paper ‘Weighted quantile estimators’.

When it comes to the analysis of a statistical significance test design, many people tend to overfocus purely on the Type I error rate.

This post addresses the challenge of scale measurement when discrete distributions cause tied values that collapse MAD to zero.

This post builds a weighted modification of the Hodges–Lehmann estimator that supports weighted samples.

Nowadays, GitHub Actions is one of the most popular free CI systems.

In our of the previous post, I explored the distribution of observed p-values for the Mann–Whitney U test in the finite case when the null hypothesis is true.

In this post, we perform a short numerical simulation to compare the statistical power of the Mann-Whitney U test and the Brunner-Munzel test under normality for various sample sizes and significance levels.

When we work with null hypothesis significance testing and the null hypothesis is true, the distribution of observed p-value is asymptotically uniform.

The Brunner–Munzel test is a nonparametric significance test, which can be considered an alternative to the Mann–Whitney U test.

The Mann–Whitney U test is one of the most popular nonparametric statistical tests.

This post classifies the different types of finite-sample consistency for robust scale estimators used as standard deviation replacements.

Imagine you work with some data and assume that the underlying distribution is approximately normal.

This post compares two nonparametric effect size variants: one consistent with Cohen’s d and one consistent with Glass’s delta.

This post proposes combining three complementary thresholds — shift, ratio, and effect size — for more reliable tests of practical significance.

This post evaluates the finite-sample Gaussian efficiency of the trimmed Hodges–Lehmann estimator.

This post studies the breakdown point of a trimmed variant of the Hodges–Lehmann estimator.

This post evaluates the Gaussian efficiency of the Hodges–Lehmann location shift estimator against the difference of sample medians.

This post demonstrates that the median of pairwise differences and the difference of sample medians can have opposite signs on multimodal distributions.

This post analyses the resistance of the Hodges–Lehmann estimator to low-density regions of a distribution.

Kernel density estimation (KDE) is a popular way to approximate a distribution based on the given data.

In the post about the importance of kernel density estimation bandwidth, I reviewed several bandwidth selectors and showed their impact on the KDE.

In the previous post, we defined the resistance function that show sensitivity of the given estimator to the low-density regions.

When we discuss resistant statistics, we typically assume resistance to extreme values.

In the previous post, we obtained the finite-sample Gaussian efficiency values of the sample median and the Harrell-Davis median.

In this post, we explore finite-sample and asymptotic Gaussian efficiency values of the sample median and the Harrell-Davis median.

Let $\mathbf{x} = \{ x_1, x_2, \ldots, x_n \}$ be a sample of size $n$.

This post announces the preprint on finite-sample properties of the Rousseeuw–Croux $S_n$ and $Q_n$ scale estimators.

In the previous posts (1, 2), I have explored the sensitivity curves of the Harrell-Davis quantile estimator on the normal distribution, the exponential distribution, and the Cauchy distribution.

In the previous post, I have explored the sensitivity curves of the Harrell-Davis quantile estimator on the normal distribution.

The Harrell-Davis quantile estimator is an efficient replacement for the traditional quantile estimator, especially in the case of light-tailed distributions.

There are various ways to estimate quantiles of weighted samples.

When we work with weighted samples, it’s essential to introduce adjustments for the sample size.

This post derives finite-sample bias-correction factors for the Rousseeuw–Croux $S_n$ and $Q_n$ estimators.

This post announces the preprint on quantile absolute deviation as a flexible robust scale estimator.

In one of the previous posts, I suggested a new measure of dispersion called the standard quantile absolute deviation around the median ($\operatorname{SQAD}$) which can be used as an alternative to the median absolute deviation ($\operatorname{MAD}$) as a

This post finds the optimal quantile level that maximises the Gaussian efficiency of the quantile absolute deviation.

In this post, we derive the exact equation for the quantile absolute deviation around the median of the Pareto(1,1) distribution.

In this post, we derive the exact equation for the quantile absolute deviation around the median of the Exponential distribution.

In this post, we derive the exact equation for the quantile absolute deviation around the median of the Uniform distribution.