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Regression Toward the Mean

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...

Bias

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
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Weighted Mean

Weighted Mean

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For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...

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Detection of Gross Error: The Q Test

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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

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Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...

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Updated: Sep 1, 2025

AMEBaS: Automatic Midline Extraction and Background Subtraction of Ratiometric Fluorescence Time-Lapses of Polarized Single Cells

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On automatic bias reduction for extreme expectile estimation.

Stéphane Girard¹, Gilles Stupfler², Antoine Usseglio-Carleve³

¹Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France.

Statistics and Computing

|August 15, 2022

Summary

This study introduces bias-reduced estimators for extreme expectiles in heavy-tailed distributions, improving risk management accuracy. These new methods offer better finite-sample performance for financial and actuarial applications.

Keywords:

Asymmetric least squares Bias reduction Expectiles Extrapolation Extremes Heavy tails Second-order parameter

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Area of Science:

Quantitative Finance
Actuarial Science
Statistical Modeling

Background:

Expectiles are gaining traction as a coherent and elicitable risk measure in finance and actuarial science.
Current extreme expectile estimators for heavy-tailed distributions suffer from bias, leading to poor performance in real-world samples.

Purpose of the Study:

To develop bias-reduced extreme expectile estimators for heavy-tailed distributions.
To improve the accuracy and finite-sample performance of risk measures in financial and actuarial applications.

Main Methods:

Investigated asymptotic proportionality between extreme expectiles and quantiles.
Utilized extrapolation formulas within a heavy-tailed context.
Quantified and estimated bias in existing extreme expectile estimation methods.
Developed and rigorously proved asymptotic properties of new bias-reduced estimators.

Main Results:

Introduced novel classes of bias-reduced extreme expectile estimators.
Demonstrated improved asymptotic and finite-sample properties compared to existing methods.
Validated findings through simulation studies and real-world data from economics, insurance, and finance.

Conclusions:

The proposed bias-reduced estimators offer a significant improvement for extreme expectile estimation in heavy-tailed distributions.
These advancements enhance the reliability of risk management tools in actuarial and financial sectors.
The study provides robust estimators suitable for practical applications with financial and insurance data.