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Asymptotics for argmin processes: Convexity arguments

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  • Kato, Kengo
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    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7 (1991) 186-199], Hjort and Pollard [N.L. Hjort, D. Pollard, Asymptotics for minimizers of convex processes, 1993 (unpublished manuscript)], and Geyer [C.J. Geyer, On the asymptotics of convex stochastic optimization, 1996 (unpublished manuscript)] are now basic tools for investigating the asymptotic behavior of M-estimators with non-differentiable convex objective functions.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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 8 (September)
    Pages: 1816-1829

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1816-1829

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    Keywords: Argmin process Convexity argument Parametrized objective function Regression quantile process Representation theorem Threshold regression;

    References

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
    4. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
    5. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, 03.
    6. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    7. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    8. Caner, Mehmet, 2002. "A Note On Least Absolute Deviation Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 18(03), pages 800-814, June.
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    Cited by:
    1. Heejoon Han & Oliver Linton & Tatsushi Oka & Yoon-Jae Whang, 2014. "The cross-quantilogram: measuring quantile dependence and testing directional predictability between time series," CeMMAP working papers CWP06/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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