Linear Regression for Heavy Tails

Guus Balkema and Paul Embrechts
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Guus Balkema: Department of Mathematics, Universiteit van Amsterdam, 1098xh Amsterdam, The Netherlands
Paul Embrechts: RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

Risks, 2018, vol. 6, issue 3, 1-70

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.

Keywords: exponential generalized beta prime; generalized beta prime; hyperbolic balance; least absolute deviation; least trimmed squares; Pareto distribution; right median; Theil–Sen; weighted balance (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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