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Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models

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  • Linton, Oliver

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 12 (1996)
Issue (Month): 01 (March)
Pages: 30-60

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Handle: RePEc:cup:etheor:v:12:y:1996:i:01:p:30-60_00

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  1. Hardle, W., 1992. "Applied Nonparametric Methods," Papers, Catholique de Louvain - Institut de statistique 9204, Catholique de Louvain - Institut de statistique.
  2. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 38(3), pages 301-339, July.
  3. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 9(04), pages 539-569, August.
  4. 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, Econometric Society, vol. 45(6), pages 1517-34, September.
  5. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  6. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  7. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 37(1), pages 81-98, February.
  8. Phillips, Peter C. B., 1977. "An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 6(2), pages 147-164, September.
  9. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 787-815, May.
  10. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  11. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
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Cited by:
  1. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2003/451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, 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, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /1999/374, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. 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.
  5. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1148, Cowles Foundation for Research in Economics, Yale University.
  6. Y Nishiyama & Peter Robinson, 1999. "Studentization in Edgworth expansions for estimates of semiparametric index models," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2095, London School of Economics and Political Science, LSE Library.
  7. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, School of Economics and Management, University of Aarhus.

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