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Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models

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Abstract

We examine the higher order asymptotic properties of semiparametric regression estimators that were obtained by the general MINPIN method described in Andrews (1989). We derive an order n^{-1} stochastic expansion and give a theorem justifying order n^{-1} distributional approximation of the Edgeworth type.

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  • Oliver Linton, 1994. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Cowles Foundation Discussion Papers 1086, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1086
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    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    2. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Phillips, Peter C. B., 1977. "An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator," Journal of Econometrics, Elsevier, vol. 6(2), pages 147-164, September.
    5. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
    6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    7. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-1534, September.
    8. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
    9. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    10. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
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    Cited by:

    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2017. "Double/Debiased Machine Learning for Treatment and Structural Parameters," NBER Working Papers 23564, National Bureau of Economic Research, Inc.
    2. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
    3. Y Nishiyama & Peter M Robinson, 1999. "Studentization in Edgworth Expansions for Estimates of Semiparametric Index Models - (Now published in C Hsiao, K Morimune and J Powell (eds): Nonlinear Statistical Modeling (Festschrift for Takeshi A," STICERD - Econometrics Paper Series 374, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers CWP04/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    6. Nishiyama, Y & Robinson, Peter, 1999. "Studentization in Edgworth expansions for estimates of semiparametric index models," LSE Research Online Documents on Economics 2095, London School of Economics and Political Science, LSE Library.
    7. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    9. repec:wly:emetrp:v:85:y:2017:i::p:233-298 is not listed on IDEAS
    10. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    11. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    12. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.

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