Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T04:05:20.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models

Published online by Cambridge University Press:  11 February 2009

Oliver Linton
Oliver Linton
Affiliation:
Yale University
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the higher order asymptotic properties of semiparametric regression estimators that were obtained by the general MINPIN method described in Andrews (1989, Semiparametric Econometric Models: I. Estimation, Discussion paper 908, Cowles Foundation). We derive an order n−1 stochastic expansion and give a theorem justifying order n−1 distributional approximation of the Edgeworth type.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 1 , March 1996 , pp. 30 - 60
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1989) Semiparametric Econometric Models: I. Estimation. Discussion paper 908, Cowles Foundation.Google Scholar
Andrews, D.W.K. (1991) Asymptotic normality of series estimators for nonparametric and semiparametric models. Econometrica 59, 307–346.CrossRefGoogle Scholar
Bhattacharya, R.N. & Ghosh, J.K. (1978) On the validity of the formal Edgeworth expansion. Annals of Statistics 6, 434–451.CrossRefGoogle Scholar
Bhattacharya, R.N. & Ranga, Rao (1976) Normal Approximation and Asymptotic Expansions. New York: Wiley.Google Scholar
Bickel, P.J. (1982) On adaptive estimation. Annals of Statistics 14, 1463–1484.Google Scholar
Bickel, P.J., Gotze, F., & van Zwet, W.R. (1986) The Edgeworth expansion for U statistics of degree two. Annals of Statistics 14, 1463–1484.Google Scholar
Bickel, P.J., Klaassen, C.A.J.Ritov, Y., & Wellner, J.A. (1994) Efficient and Adaptive Inference in Semiparametric Models. Baltimore, Maryland: Johns Hopkins University Press.Google Scholar
Callaert, H., Janssen, P., & Veraverbeke, N. (1980) An Edgeworth expansion for U-statistics. Annals of Statistics 8, 299–312.Google Scholar
Carroll, R.J. (1982) Adapting for heteroscedasticity in linear models. Annals of Statistics 10, 1224–1233.Google Scholar
Carroll, R.J. & Hall, P. (1989) Variance function estimation in regression: The effect of estimating the mean. Journal of the Royal Statistical Society, Series B 51, 3–14.Google Scholar
Chen, H. (1988) Convergence rates for parametric components in a partly linear model. Annals of Statistics 16, 136–146.CrossRefGoogle Scholar
Chesher, A. & Spady, R. (1991) Asymptotic expansion of the information test. Econometrica 59, 787–816.Google Scholar
Gotze, F. (1987) Approximations for multivariate U statistics. Journal of Multivariate Analysis 22, 212–229.CrossRefGoogle Scholar
Hardle, W. (1990) Applied Nonparametric Regression. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hardle, W. & Linton, O.B. (1994) Applied nonparametric methods. In Engle III, R.F. & McFadden, D. (eds.), The Handbook of Econometrics, vol. 4, pp. 2295–2339. Amsterdam: North Holland.CrossRefGoogle Scholar
Hardle, W. & Stoker, T.M. (1989) Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84, 986–995.Google Scholar
Hsieh, D.A. & Manski, C.F. (1987) Monte Carlo evidence on adaptive maximum likelihood estimation of a regression. Annals of Statistics 15, 541–551.CrossRefGoogle Scholar
Lee, A.J. (1990) U-Statistics: Theory and Practice. New York: Marcel Dekker.Google Scholar
Linton, O.B. (1991) Edgeworth Approximation in Semiparametric Regression Models. Ph.D. Thesis, Department of Economics, University of California, Berkeley.Google Scholar
Linton, O.B. (1993a) Adaptive estimation in ARCH models. Econometric Theory 9, 539–570.Google Scholar
Linton, O.B. (1993b) Second order approximation in a linear regression with heteroskedastic-ity of unknown form. Econometric Reviews, forthcoming.Google Scholar
Linton, O.B. (1995) Second order approximation in the partially linear model. Econometrica 63, 1079–1113.CrossRefGoogle Scholar
McCullagh, P. (1989) Tensor Methods in Statistics. Chapman and Hall.Google Scholar
Manski, C.F. (1984) Adaptive estimation of non-linear regression models. Econometric Reviews 3, 145–194.CrossRefGoogle Scholar
Mikosch, T. (1991) Functional limit theorems for random quadratic forms. Stochastic Processes and Their Application 37, 81–98.Google Scholar
Miiller, H.G. (1988) Nonparametric regression analysis of longitudinal data. In Lecture Notes in Statistics, vol. 46. Heidelberg, New York: Springer-Verlag.Google Scholar
Newey, W.K. (1988) Adaptive estimation of regression models via moment restrictions. Journal of Econometrics 38, 301–339.CrossRefGoogle Scholar
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99–135.CrossRefGoogle Scholar
Pfanzagl, J. (1973) Asymptotic expansions related to minimum contrast estimators. Annals of Statistics 1, 993–1026.Google Scholar
Pfanzagl, J. (1980) Asymptotic expansions in parametric statistical theory. In Krishnaiah, P.R. (ed.), Developments in Statistics, vol. 3, pp. 1–97. New York: Academic Press.Google Scholar
Phillips, P.C.B. (1977a) An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator. Journal of Econometrics 6, 147–164.CrossRefGoogle Scholar
Phillips, P.C.B. (1977b) A general theorem in the theory of asymptotic expansions as approximations to the finite sample distributions of econometric estimators. Econometrica 45, 463–485.CrossRefGoogle Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.CrossRefGoogle Scholar
Robinson, P.M. (1987) Asymptotically efficient estimation in the presence of heteroscedastic-ity of unknown form. Econometrica 56, 875–891.Google Scholar
Robinson, P.M. (1988a) The stochastic difference between econometric statistics. Econometrica 56, 531–548.CrossRefGoogle Scholar
Robinson, P.M. (1988b) Root-/V-consistent semiparametric regression. Econometrica 56, 931–954.CrossRefGoogle Scholar
Robinson, P.M. (1988c) Semiparametric econometrics: A survey. Journal of Applied Econometrics 3, 35–51.CrossRefGoogle Scholar
Robinson, P.M. (1991a) Automatic frequency domain inference on semiparametric and. non-parametric models. Econometrica 59, 1329–1364.Google Scholar
Robinson, P.M. (1991b) Best nonlinear three-stage least squares estimation of certain econometric models. Econometrica 59, 755–786.CrossRefGoogle Scholar
Rothenberg, T.J. (1984) Approximate normality of generalized least squares estimates. Econometrica 52, 811–825.CrossRefGoogle Scholar
Rothenberg, T.J. (1986) Approximating the distribution of econometric estimators and test statistics. In Griliches, Z. & lntriligator, M.D. (eds.), Handbook of Econometrics, vol. 2, pp. 881–935. Amsterdam: North-Holland.CrossRefGoogle Scholar
Sargan, J.D. (1976) Econometric estimators and the Edgeworth expansion. Econometrica 44, 421–448.Google Scholar
Skovgaard, I.M. (1981) Edgeworth expansions of the distributions of maximum likelihood estimators in the general case. Scandinavian Journal of Statistics 10, 227–236.Google Scholar
Stock, J.H. (1989) Nonparametric policy analysis. Journal of the American Statistical Association 84, 567–576.Google Scholar
Stoker, T.M. (1991) Smoothing bias in derivative estimation. Journal of the American Statistical Association, forthcoming.Google Scholar