Next Article in Journal
Country Risk Ratings and Stock Market Returns in Brazil, Russia, India, and China (BRICS) Countries: A Nonlinear Dynamic Approach
Previous Article in Journal
On the Basel Liquidity Formula for Elliptical Distributions
Previous Article in Special Issue
Precise Large Deviations for Subexponential Distributions in a Multi Risk Model
Article Menu

Export Article

Open AccessArticle
Risks 2018, 6(3), 93; https://doi.org/10.3390/risks6030093

Linear Regression for Heavy Tails

1
Department of Mathematics, Universiteit van Amsterdam, 1098xh Amsterdam, The Netherlands
2
RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
Received: 29 June 2018 / Revised: 18 August 2018 / Accepted: 21 August 2018 / Published: 10 September 2018
(This article belongs to the Special Issue Heavy Tailed Distributions in Economics)
Full-Text   |   PDF [3893 KB, uploaded 11 September 2018]   |  

Abstract

There exist several estimators of the regression line in the simple linear regression: Least Squares, Least Absolute Deviation, Right Median, Theil–Sen, Weighted Balance, and Least Trimmed Squares. Their performance for heavy tails is compared below on the basis of a quadratic loss function. The case where the explanatory variable is the inverse of a standard uniform variable and where the error has a Cauchy distribution plays a central role, but heavier and lighter tails are also considered. Tables list the empirical sd and bias for ten batches of one hundred thousand simulations when the explanatory variable has a Pareto distribution and the error has a symmetric Student distribution or a one-sided Pareto distribution for various tail indices. The results in the tables may be used as benchmarks. The sample size is n = 100 but results for n = are also presented. The error in the estimate of the slope tneed not be asymptotically normal. For symmetric errors, the symmetric generalized beta prime densities often give a good fit. View Full-Text
Keywords: exponential generalized beta prime; generalized beta prime; hyperbolic balance; least absolute deviation; least trimmed squares; Pareto distribution; right median; Theil–Sen; weighted balance exponential generalized beta prime; generalized beta prime; hyperbolic balance; least absolute deviation; least trimmed squares; Pareto distribution; right median; Theil–Sen; weighted balance
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Balkema, G.; Embrechts, P. Linear Regression for Heavy Tails. Risks 2018, 6, 93.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top