Second order approximation in a linear regression with heteroskedasticity of unknown form

Econometric Reviews

Volumn 15, Issue 1, 1996, Pages 1-32

  Linton, Oliver B ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Asymptotic expansions; Gls; Heteroskedasticity; Local linear regression; Semiparametric estimation

Indexed keywords

EID: 0007073768     PISSN: 07474938     EISSN: 15324168     Source Type: Journal    
DOI: 10.1080/07474939608800336     Document Type: Article

References (53)

1. Anand S., Harris C., Linton O., On the concept of Ultrapoverty Harvard Center for Population 1993 working paper no 9302
2. Anderson, T. W., and Sawa, T., 1979. Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate. Econometrica, 47: 163–182.
3. Andrews D.W.K., Semiparametric Econometric Models: I Estimation 1989a Cowles Foundation Discussion paper no. 908
4. Andrews D.W.K., Semiparametric Econometric Models: II Estimation 1989b Cowles Foundation Discussion paper no. 910
5. Andrews, D. W. K., 1991a. Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models. Econometrica, 59: 307–346.
6. Andrews, D. W. K., 1991b. Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59: 817–858.
7. Carroll, R. J., 1982. Adapting for Heteroscedasticity in Linear Models. Annals of Statistics, 10: 1224–1233.
8. Carrol, R. J., and Härdle, W., 1989. Second Order Effects in Semiparametric Weighted Least Squares Regression. Statistics, 2: 179–186.
9. Carrol, R. J., Wu, C. F., and Ruppert, D., 1988. The Effect of Estimating Weights in Weighted Least Squares. Journal of the American Statistical Association, 83: 1045–1054.
10. Cavanagh, C. J., 1989. “ The Cost of Adapting for Heteroskedasticity in Linear Regression Models ”. Harvard University. Unpublished Manuscript
11. Chesher, A., and Jewitt, I., 1987. The Bias of a Heteroskedasticity Consistent Covariance Matrix. Econometrica, 55: 1217–1222.
12. Chesher, A., 1989. Hajek Inequalities, Measures of Leverage and the Size of Heteroskedasticity Robust Wald Tests. Econometrica, 57: 971–977.
13. Cox, D. R., and Hinkley, D. V., 1974. Theoretical Statistics, Chapman and Hall.
14. Cox, D. R., 1980. Local ancillarity. Biometrika, 67: 279–286.
15. Eicker, F., 1968. Asymptotic Normality and Consistency of the Least Squares Regression Model for Families of Linear Regressions. Annals of Mathematical Statistics, 34: 447–456.
16. Fan, J., 1992. Design-Adaptive Nonparametric Regression. Journal of the American Statistical Association, 87: 998–1004.
17. Fan, J., and Gijbels, I., 1992. “ Spatial and Design Adaptation: Adaptive Order Polynomial Approximation in Function Estimation ”. Core. Manuscript
18. Härdle, W., Hart, J., Marron, J. S., and Tsybakov, A. B., 1992. Bandwidth Choice for Average Derivative Estimation. Journal of the American Statistical Association, 87: 218–226.
19. Härdle, W., and Linton, O., 1993. “ Applied nonparametric methods ”. In The Handbook of Econometrics, Edited by: McFadden, D. F., and Engle, R. F., III. Vol. IV, North Holland.
20. Hsieh, D. A., and Manski, C. F., 1987. Monte Carlo Evidence on Adaptive Maximum Likelihood Estimation of a Regression. Annals of Statistics, 15: 541–551.
21. Lee, A. J., 1990. U-Statistics: Theory and Practice, Marcel Dekker.
22. Linton, O. B., 1991. Edgeworth Approximation in Semiparametric Regression Models, Department of Economics DC Berkeley. PhD thesis
23. Linton O. B., Edgeworth Approximation for Generalised Minimum Contrast Estimators in Semiparametric Regression Models 1992 Nuffield College Discussion Paper no. 73
24. Linton O. B., Second Order Approximation in the Partially Linear Model 1993 Cowles Foundation Discussion Paper no 1065
25. Linton, O. B., and Nielskn, J. P., 1994. A Multiplicative Bias Reduction Method for Nonparametric Regression. Statistics and Probability Letters, 19: 181–187.
26. Müller, H. G., 1988. “ Lecture Notes in Statistics ”. In Nonparametric Regression Analysis of Longitudinal Data, Vol. 46, Heidelberg, New York: Springer-Verlag.
27. Müller, H. G., and Stadtmüller, U., 1987. Estimation of Heteroskedasticity in Regression Analysis. Annals of Statistics, 15: 610–625.
28. Nagar, A. L., 1959. The Bias and Moment Matrix of the General k-Class Estimators of the Parameters in Simultaneous Equations. Econometrica, 27: 575–595.
29. Newey, W. K., 1990a. Semiparametric Efficiency Bounds. Journal of Applied Econometrics, 5: 99–135.
30. Newey, W. K., 1990b. Efficient Instrumental Variables Estimation of Nonlinear Models. Econometrica, 58: 809–837.
31. Park, B. U., and Marron, J. S., 1990. Comparison of Data-Driven Bandwidth Selectors. Journal of the A merican Statistical Association, 85: 66–72.
32. Phillips, P. C. B., 1977a. A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators. Econometrica, 45: 1517–1534.
33. Phillips, P. C. B., 1977b. An Approximation to the Finite Sample Distribution of Zellner's Seemingly Unrelated Regression Estimator. Econometrica, 6: 147–164.
34. Robinson, P. M., 1987. Asymptotically Efficient Estimation in the Presence of Heteroscedasticity of Unknown form. Econometrica, 56: 875–891.
35. Robinson, P. M., 1988a. The Stochastic Difference between Econometric Statistics. Econometrica, 56: 531–548.
36. Robinson, P. M., 1988b. Root-N-Consistent Semiparametric Regression. Econometrica, 56: 931–954.
37. Robinson, P. M., 1991a. Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models. Econometrica, 59: 1329–1364.
38. Robinson, P. M., 1991b. Best Nonlinear Three-stage Least Squares Estimation of certain Econometric Models. Econometrica, 59: 755–786.
39. Rothenberg, T., 1984a. “ Approximating the Distributions of Econometric Estimators and Test Statistics ”. In Handbook of Econometrics, Edited by: Grilliches, Z., and Intriligator, M., Vol. 2, North Holland. Ch. 14
40. Rothenberg, T., 1984b. Approximate Normality of Generalized Least Squares Estimates. Econometrica, 52: 811–825.
41. Rothenberg, T., 1988. Approximate Power Functions for some Robust Tests of Regression Coefficients. Econometrica, 56: 997–1019.
42. Ruppert, D., and Wand, M. P., 1992. Multivariate Weighted Least Squares Regression, Rice University. Department of Statistics Technical Report no 92-4
43. Sargan, J. D., and Mikhail, W. M., 1971. A General Approximation to the Distribution of Instrumental Variables Estimates. Econometrica, 39: 131–169.
44. Sargan, J. D., 1975. Gram-Charlier Approximations Applied to t Ratios of k-Class Estimators. Econometrica, 43: 327–346.
45. Sargan, J. D., 1976. Econometric Estimators and the Edgeworth Approximation. Econometrica, 44: 421–448.
46. Sheather, S. J., and Jones, M. C., 1991. A Reliable Data-based Bandwidth Selection Method for Kernel Density Estimation. Journal of the Royal Statistical Society, 53: 683–690. Series B
47. Silverman, B., 1986. Density estimation for statistics and data analysis, London: Chapman and Hall.
48. Stock, J. H., 1989. Nonparametric Policy Analysis. Journal of the American Statistical Association, 84: 567–576.
49. Stock, J. H., 1991. “ Nonparametric Policy Analysis: An Application to Estimating Hazardous Waste Cleanup Benefits ”. In Nonparametric and Semiparametric Methods in Econometrics and Statistics Edited by: Barnett, Powell., and Tauchen.
50. Stoker, T., 1989. Tests of Average Derivative Constraints. Review of Economic Studies, 56: 535–552.
51. Stoker, T. M., 1993. Smoothing Bias in Derivative Estimation. Journal of the A merican Statistical Association, 56 Forthcoming in
52. Stone, C. J., 1977. Consistent Nonparametric Regression. Annals of Statistics, 5: 595–620.
53. White, H., 1980. A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica, 48: 817–838.