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Edgeworth Approximations for Semiparametric Instrumental Variable Estimators and Test Statistics

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Author Info
Oliver Linton

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Abstract

We stablish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We emply local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n -? for some 0 < ? < ½, where ? depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/399.

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Date of creation: Jul 2000
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Handle: RePEc:cep:stiecm:/2000/399

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Related research
Keywords: Bandwidth selection; Edgeworth approximation; instrumental viariables; kernel estimation; local polynomials.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. J. L. Horowitz, . "Bootstrap Methods In Econometrics: Theory And Numerical Performance," Sonderforschungsbereich 373 1995-63, Humboldt Universitaet Berlin.
  2. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May. [Downloadable!] (restricted)
  3. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier. [Downloadable!] (restricted)
  4. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July. [Downloadable!] (restricted)
  5. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July. [Downloadable!] (restricted)
  6. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-80, May. [Downloadable!] (restricted)
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  8. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December. [Downloadable!] (restricted)
  9. Hua, Liang & Ping, Cheng, 1993. "Second order asymptotic efficiency in a partial linear model," Statistics & Probability Letters, Elsevier, vol. 18(1), pages 73-84, August. [Downloadable!] (restricted)
  10. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
  11. Oliver Linton, 1996. "Second order approximation in a linear regression with heteroskedasticity of unknown form," Econometric Reviews, Taylor and Francis Journals, vol. 15(1), pages 1-32. [Downloadable!] (restricted)
  12. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-37, July. [Downloadable!] (restricted)
  13. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996. [Downloadable!]
  14. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-83, September. [Downloadable!] (restricted)
    Other versions:
  15. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December. [Downloadable!] (restricted)
  16. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July. [Downloadable!] (restricted)
  17. Oliver Linton, 1994. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Cowles Foundation Discussion Papers 1086, Cowles Foundation, Yale University. [Downloadable!]
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  18. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  19. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-86, May. [Downloadable!] (restricted)
  20. repec:cup:etheor:v:12:y:1996:i:1:p:30-60 is not listed on IDEAS
  21. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation, Yale University. [Downloadable!]
  22. Haerdle,W. & Marron,J.S., 1989. "Bootstrap simultaneous error bars for nonparametric regression," Discussion Paper Serie A 227, University of Bonn, Germany.
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  23. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July. [Downloadable!] (restricted)
    Other versions:
  24. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  25. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March. [Downloadable!] (restricted)
  26. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July. [Downloadable!] (restricted)
  27. Götze, F., 1987. "Approximations for multivariate U-statistics," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 212-229, August. [Downloadable!] (restricted)
  28. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September. [Downloadable!] (restricted)
    Other versions:
  29. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  30. Oliver Linton, 1997. "Second-Order Approximation for Semiparametric Instrumental Variable Estimators and Test Statistics," Cowles Foundation Discussion Papers 1151, Cowles Foundation, Yale University. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series /2003/451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  2. Liangjun Su & Halbert White, 2004. "Testing Conditional Independence Via Empirical Likelihood," University of California at San Diego, Economics Working Paper Series 2003-14, Department of Economics, UC San Diego. [Downloadable!]
  3. Liangjun Su & Halbert White, 2003. "A Consistent Characteristic-Fuction-Based Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series 2003-11, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
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