Posts on Andrey Akinshin

In the previous post, we have obtained a nice version of the trimmed Harrell-Davis quantile estimator which provides an opportunity to get a nice trade-off between robustness and statistical efficiency of quantile estimations.

In one of the previous posts, I discussed the idea of the trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width.

In the previous post, we have discussed the trimmed modification of the Harrell-Davis quantile estimator based on the highest density interval of size $\sqrt{n}/n$.

In the previous post, we have obtained a nice quantile estimator.

In my previous post, I tried the idea of using the trimmed modification of the Harrell-Davis quantile estimator based on the highest density interval of the given width.

During the last several months, I have been experimenting with different variations of the trimmed Harrell-Davis quantile estimator.

In the previous posts, I discussed various aspects of quantile estimators based on k order statistics.

In the previous two posts, I discussed the idea of quantile estimators based on k order statistics.

In the previous post, I described the idea of using quantile estimators based on k order statistics.

It’s not easy to choose a good quantile estimator.

Previously, I already discussed the trimmed modification of the Harrell-Davis quantile estimator several times.

The traditional quantile estimators (which are based on 1 or 2 order statistics) have great robustness.

When it comes to estimating quantiles of the given sample, my estimator of choice is the Harrell-Davis quantile estimator (to be more specific, its trimmed version).

In my previous posts, I described how to calculate weighted quantiles and their confidence intervals using the Harrell-Davis quantile estimator.

Let’s start with a problem from real life.

This post handles the corner case where MAD collapses to zero, causing the gamma effect size formula to break down.

When we collect software performance measurements, we get a bunch of time intervals.

This post extends the nonparametric Cohen’s d-consistent effect size with customization options for different practical requirements.

Statistical efficiency is a common measure of the quality of an estimator.

Let’s say we want to estimate the median based on a small sample (3 $\leq n \leq 7$) from a right-skewed heavy-tailed distribution with high statistical efficiency.

In the previous posts, I discussed the statistical efficiency of different quantile estimators (Efficiency of the Harrell-Davis quantile estimator and Efficiency of the winsorized and trimmed Harrell-Davis quantile estimators).

In this previous post, I showed how to apply exponential smoothing to quantiles using the weighted Harrell-Davis quantile estimator.

One of the popular problems in time series analysis is estimating the moving “average” value.

In my previous posts, I already discussed the problem that arises when we try to build kernel density estimation (KDE) for samples with ties.

Update (2024-03-19): A better approach is presented in [[discrete-sample-jittering2]] Let’s say you have a sample with tied values.

Kernel density estimation (KDE) is a popular technique of data visualization.

In previous posts, I suggested two modifications of the Harrell-Davis quantile estimator: winsorized and trimmed.

In one of the previous posts, I discussed winsorized Harrell-Davis quantile estimator.

One of the most essential properties of a quantile estimator is its efficiency.

The Navruz-Özdemir quantile estimator suggests the following equation to estimate the $p^\textrm{th}$ quantile of sample $X$: $$ \begin{split} \operatorname{NO}_p = & \Big( (3p-1)X_{(1)} + (2-3p)X_{(2)} - (1-p)X_{(3)} \Big) B_0 +\\ & +\sum_{i=1}^n \Big((1…

There are dozens of different ways to estimate quantiles.

The Harrell-Davis quantile estimator is one of my favorite quantile estimators because of its efficiency.

This post demonstrates with concrete examples how the standard deviation can be entirely misleading even for minor deviations from normality.

This post improves MAD bias-correction by using the Harrell-Davis quantile estimator for the inner median, achieving better finite-sample behaviour.

This post derives finite-sample bias-correction factors for MAD to make it a consistent estimator of the standard deviation.

This post applies the gamma effect size to practical case studies comparing performance distributions across quantiles.

This post demonstrates how a single outlier can completely distort Cohen’s d, and compares it with a nonparametric alternative.

Update: the latest version of this approach is presented in [[partitioning-heaps-quantile-estimator3]].

In one of the previous posts, I described the P² quantile estimator.

This case study evaluates the accuracy of MAD estimation using the Harrell-Davis quantile estimator on Gumbel-distributed data.

Update: the latest version of this approach is presented in [[partitioning-heaps-quantile-estimator3]].

There is a common misunderstanding that a 95% confidence interval is an interval that covers the true parameter value with 95% probability.

Software performance is a complex discipline that requires knowledge in different areas from benchmarking to the internals of modern runtimes, operating systems, and hardware.

Update 2021-07-06: the approach was updated using the Kish’s effective sample size.

This post introduces the quantile absolute deviation (QAD) for measuring dispersion around arbitrary quantiles.

Imagine that you are implementing performance telemetry in your application.

Let’s say you collected a lot of data and want to explore the underlying distributions of collected samples.

Outlier analysis is a typical step in distribution exploration.

Multimodality is an essential feature of a distribution, which may create many troubles during automatic analysis.

The idea of this post was born when I was working on a presentation for my recent DotNext talk.