Asymptotics for argmin processes: Convexity arguments

Kengo Kato

Journal of Multivariate Analysis, 2009, vol. 100, issue 8, 1816-1829

Abstract: The convexity arguments developed by Pollard [D. Pollard, Asymptotics for least absolute deviation regression estimators, Econometric Theory 7 (1991) 186-199], Hjort and Pollard [N.L. Hjort, D. Pollard, Asymptotics for minimizers of convex processes, 1993 (unpublished manuscript)], and Geyer [C.J. Geyer, On the asymptotics of convex stochastic optimization, 1996 (unpublished manuscript)] are now basic tools for investigating the asymptotic behavior of M-estimators with non-differentiable convex objective functions. This paper extends the scope of convexity arguments to the case where estimators are obtained as stochastic processes. Our convexity arguments provide a simple proof for the asymptotic distribution of regression quantile processes. In addition to quantile regression, we apply our technique to LAD (least absolute deviation) inference for threshold regression.

Keywords: Argmin; process; Convexity; argument; Parametrized; objective; function; Regression; quantile; process; Representation; theorem; Threshold; regression (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (32)

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