An Expectile Strong Law of Large Numbers

Collin Philipps (collin.philipps@afacademy.af.edu)
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Collin Philipps: Department of Economics and Geosciences, US Air Force Academy

No 2022-05, Working Papers from Department of Economics and Geosciences, US Air Force Academy

Abstract: We show that Kolmogorov's classical strong law of large numbers applies to all expectiles uniformly. The expectiles of a random sample converge almost surely (uniformly) to the true expectiles if and only if the true data generating process has a finite first moment. The result holds for expectile functions of scalar and vector-valued random variables and can be reformulated to state that the mean (or any expectile) of a random sample converges almost surely to the true mean (or expectile) if and only if any arbitrary expectile exists and is finite.

Keywords: Expectile Regression; Quantile Regression; Strong Law of Large Numbers (search for similar items in EconPapers)
JEL-codes: C0 C21 C46 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2022-07
New Economics Papers: this item is included in nep-ecm
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