Posts on Andrey Akinshin

In [[carling-outlier-detector]], I evaluated the probability of outlier detection for samples from the Normal distribution across different outlier detectors.

This post presents a fast O(n log n) algorithm for computing the Shamos estimator via Monahan-style selection.

This post presents the Monahan algorithm for computing the Hodges–Lehmann estimator in O(n log n) time, making it practical for large samples.

Previous posts explored fast implementations of moving quantiles based on partitioning heaps: [[partitioning-heaps-quantile-estimator|Part 1]], [[partitioning-heaps-quantile-estimator2|Part 2]].

In this short case study, we explore a few more plots with Gaussian efficiency plots for the trimmed and winsorized mean estimators against the sample median.

This post explores the idea of iteratively mixing mean, median, and geometric mean, inspired by xkcd #2435.

This post evaluates the statistical efficiency of the tau measure of location — a weighted mean based on a robust scale estimate.

We continue exploring various use cases of the [[lowland-multimodality-detection]].

We continue exploring various corner cases for the [[lowland-multimodality-detection]].

When researchers focus on model design, they often worry whether the model is correct or not.

I have just published a preprint of a paper ‘Quantile-Respectful Density Estimation Based on the Harrell-Davis Quantile Estimator’.

In [[discrete-sample-jittering2]], I discussed the jittering approach that improves [[qrde]] for discrete distributions and continuous-discrete mixtures.

I continue the topic of [[qrde]] in the context of [[multimodality-detection]].

In [[discrete-sample-jittering]], I proposed a jittering approach.

This post examines how asymmetric distributions challenge Cohen’s d and its nonparametric analogues.

Statistics is one of the most confusing, controversial, and depressing disciplines I know.

If you are curious if something impacts something else, the answer is probably “yes.”

Imagine a city mayor considering a project offering to build parks in several neighborhoods.

Translation of the buisness goals to the actual parameters of the statistical procedure is a non-trivial task.

Let’s say we have two data samples, and we want to check if there is a difference between them.

I continue building a weighted version of the Mann–Whitney $U$ test.

Mann-Whitney is one of the most popular non-parametric statistical tests.

In the world of mathematical statistics, there is a constant confrontation between adepts of different paradigms.

Change point detection (CPD) in time series analysis is an essential tool for identifying significant shifts in data patterns.

[[p2-quantile-estimator]] is a streaming quantile estimator with $\mathcal{O}(1)$ memory footprint and an extremely fast update procedure.

This post clarifies the difference between the Hodges–Lehmann ratio estimator and Bhattacharyya’s scale ratio, correcting a misattribution found in several papers.

This post compares the finite-sample Gaussian efficiency of the Shamos estimator and the Rousseeuw–Croux $Q_n$.

When we choose a change point detection algorithm, the most important thing is to clearly understand why we want to detect the change points.

The usefulness and meaningfulness of the violin plots are dubious (e.g., see this video and the corresponding discussion).

We consider a problem of change point detection at the end of a time series.

Previously, I have discussed the topic of the resistance to the low-density regions of various estimators including the Hodges-Lehmann location estimator ($\operatorname{HL}$).

This post compares the efficiency of the Mean, Sample Median, and Hodges–Lehmann estimator under heavy-tailed distributions.

This post discusses how to meaningfully compare the efficiency of estimators under heavy-tailed distributions, where variance-based efficiency breaks down.

This post compares the finite-sample Gaussian efficiency of the QAD estimator against the Rousseeuw–Croux $S_n$ and $Q_n$.

Mann-Whitney U test is a good nonparametric test, which mostly targets changes in locations.

The Ansari-Bradley test is a popular rank-based nonparametric test for a difference in scale/dispersion parameters.

Previously, I already discussed the Cucconi test.

This post applies the weighted Hodges–Lehmann estimator to mixture distributions, studying how well it tracks the dominant component.

Let us consider the classic problem of outlier detection in one-dimensional sample.

It is inconvenient to work with samples from a distribution of unknown form.

This post compares the Gaussian efficiency of the two-sample Hodges–Lehmann shift estimator against applying the one-sample estimator to each group separately.

In the old times of applied statistics existence, all statistical experiments used to be performed by hand.

This post introduces a ratio estimator for multiplicative differences between two samples, built on the Hodges–Lehmann framework via a log-exp transform.

Previously, I suggested a weighted version of the Mann–Whitney $U$ test.

The Cucconi test is a nonparametric two-sample test that compares both location and scale.

Recently, I started writing about defensive statistics.

Recently, I was rereading [[hampel-robust-statistics]] and I found this quote about the difference between robust and nonparametric statistics (page 9): Robust statistics considers the effects of only approximate fulfillment of assumptions, while nonparam…

Robust statistics is a practical and pragmatic branch of statistics.

This post investigates effect size measures for multimodal distributions, where standard approaches based on mean differences fail.

In R, we have functions to calculate the density, distribution function, and quantile function of the Wilcoxon Signed Rank statistic distribution: dsignrank, psignrank, and qsignrank.