Linear Regression for Heavy Tails
AbstractThere 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
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Balkema, G.; Embrechts, P. Linear Regression for Heavy Tails. Risks 2018, 6, 93.
Balkema G, Embrechts P. Linear Regression for Heavy Tails. Risks. 2018; 6(3):93.Chicago/Turabian Style
Balkema, Guus; Embrechts, Paul. 2018. "Linear Regression for Heavy Tails." Risks 6, no. 3: 93.
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