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Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form

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Abstract

We develop stochastic expansions with remainder oP(n-2 mu), where 0

Suggested Citation

  • Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1151
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    1. Chesher, Andrew, 1989. "Hajek Inequalities, Measures of Leverage and the Size of Heteroskedasticity Robust Wald Tests," Econometrica, Econometric Society, vol. 57(4), pages 971-977, July.
    2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    3. 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.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. 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.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    8. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    9. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-825, July.
    10. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    11. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
    12. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    13. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, September.
    14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    15. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    16. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-169, January.
    17. 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.
    18. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    19. Sargan, J D, 1975. "Gram-Charlier Approximations Applied to t Ratios of k-Class Estimators," Econometrica, Econometric Society, vol. 43(2), pages 327-346, March.
    20. Anderson, T W & Sawa, Takamitsu, 1979. "Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate," Econometrica, Econometric Society, vol. 47(1), pages 163-182, January.
    21. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    22. 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.
    23. Hardle, W. & Hart, J. & Marron, J. & Tsybakov, A., 1991. "Bandwidth choice for average derivative estimation," LIDAM Discussion Papers CORE 1991049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-786, May.
    25. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, September.
    26. Linton, Oliver & Nielsen, Jens Perch, 1994. "A multiplicative bias reduction method for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 181-187, February.
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    Cited by:

    1. Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 145-174.
    2. Peter C.B. Phillips & Binbin Guo & Zhijie Xiao, 2002. "Efficient Regression in Time Series Partial Linear Models," Cowles Foundation Discussion Papers 1363, Cowles Foundation for Research in Economics, Yale University.

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