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Second Order Approximation in the Partially Linear Regression Model

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Author Info
Oliver Linton (Cowles Foundation, Yale University)

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Abstract

We examine the second order properties of various quantities of interest in the partially linear regression model. We obtain a stochastic expansion with remainder o_{P}(n^{-2mu}), where mu < 1/2, for the standardized semiparametric least squares estimator, a standard error estimator, and a studentized statistic. We use the second order expansions to correct the standard error estimates for second order effects, and to define a method of bandwidth choice. A Monte Carlo experiment provides favorable evidence on our method of bandwidth choice.

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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1065.

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Length: 47 pages
Date of creation: Dec 1993
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Publication status: Published in Econometrica (September 1995), 63(5): 1079-1112
Handle: RePEc:cwl:cwldpp:1065

Note: CFP 915.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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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. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May. [Downloadable!] (restricted)
  2. 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)
  3. 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)
  4. Haerdle,W. & Hart,J.D. & Marron,J.S. & Tsybakov,A.B., 1989. "Bandwidth choice for average derivative estimation," Discussion Paper Serie A 200, University of Bonn, Germany.
    Other versions:
  5. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," CORE Discussion Papers 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Peter C.B. Phillips & Joon Y. Park, 1986. "On the Formulation of Wald Tests of Nonlinear Restrictions," Cowles Foundation Discussion Papers 801, Cowles Foundation, Yale University. [Downloadable!]
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  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. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-25, July. [Downloadable!] (restricted)
  9. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June. [Downloadable!] (restricted)
  10. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September. [Downloadable!] (restricted)
  11. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  12. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September. [Downloadable!] (restricted)
  13. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun. [Downloadable!] (restricted)
  14. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January. [Downloadable!] (restricted)
  15. Herman Bierens & Hettie Pott-Buter, 1990. "Specification of household engel curves by nonparametric regression," Econometric Reviews, Taylor and Francis Journals, vol. 9(2), pages 123-184. [Downloadable!] (restricted)
  16. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  17. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  18. 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)
  19. Delgado, Miguel A & Stengos, Thanasis, 1994. "Semiparametric Specification Testing of Non-nested Econometric Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 291-303, April. [Downloadable!] (restricted)
  20. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
    Other versions:
  21. Robinson, P M, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 511-34, October. [Downloadable!] (restricted)
  22. repec:att:wimass:19901 is not listed on IDEAS
  23. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July. [Downloadable!] (restricted)
  24. Carroll,R. & Haerdle,W., 1988. "Second order effects in semiparametric weighted least squares regression," Discussion Paper Serie A 170, University of Bonn, Germany.
  25. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-69, January.
  26. Newey, Whitney K & Powell, James L & Walker, James R, 1990. "Semiparametric Estimation of Selection Models: Some Empirical Results," American Economic Review, American Economic Association, vol. 80(2), pages 324-28, May. [Downloadable!] (restricted)
  27. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-22, September. [Downloadable!] (restricted)
  28. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May. [Downloadable!] (restricted)
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(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. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2004. "Testing forward exchange rate unbiasedness efficiently: a semiparametric approach," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 325-353, November. [Downloadable!]
  2. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639. [Downloadable!]
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  3. Chen, Xiaohong & Pouzo, Demian, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Working Papers 38, Yale University, Department of Economics. [Downloadable!]
  4. Peter C.B. Phillips & Binbin Guo & Zhijie Xiao, 2002. "Efficient Regression in Time Series Partial Linear Models," Cowles Foundation Discussion Papers 1363, Cowles Foundation, Yale University. [Downloadable!]
  5. Xiaohong Chen & Demian Pouzo, 2008. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP09/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  6. Zhijie Xiao & Peter C.B. Phillips, 1998. "Higher Order Approximations for Wald Statistics in Cointegrating Regressions," Cowles Foundation Discussion Papers 1192, Cowles Foundation, Yale University. [Downloadable!]
  7. Peter C. B. Phillips, 2006. "Optimal Estimation of Cointegrated Systems with Irrelevant Instruments," Cowles Foundation Discussion Papers 1547, Cowles Foundation, Yale University. [Downloadable!]
  8. Xiaohong Chen & Demian Pouzo, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP20/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  9. Wolfgang Haerdle & Oliver Linton & Qihua Wang, 2003. "Semiparametric Regression Analysis under Imputation for Missing Response Data," STICERD - Econometrics Paper Series /2003/454, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  10. M. Dolores de Prada & Luis M. Borge, 1997. "Some methods for comparing first-order asymptotically equivalent estimators," Investigaciones Economicas, Fundación SEPI, vol. 21(3), pages 473-500, September. [Downloadable!]
  11. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, School of Economics and Management, University of Aarhus. [Downloadable!]
  12. 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!]
  13. Xiaohong Chen & Demian Pouzo, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Cowles Foundation Discussion Papers 1640R, Cowles Foundation, Yale University, revised Jul 2009. [Downloadable!]
  14. Oliver Linton, 2000. "Edgeworth Approximations for Semiparametric Instrumental Variable Estimators and Test Statistics," STICERD - Econometrics Paper Series /2000/399, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  15. 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!]
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  16. Qihua Wang & Oliver Linton & Wolfgang Hardle, 2003. "Semiparametric regression analysis with missing response at random," CeMMAP working papers CWP11/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  17. Yingcun Xia & Wolfgang Härdle & Oliver Linton, 2009. "Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator," SFB 649 Discussion Papers SFB649DP2009-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  18. Mototsugu Shintani & Oliver Linton, 2000. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," Working Papers 0111, Department of Economics, Vanderbilt University, revised Jun 2001. [Downloadable!]
    Other versions:
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