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Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals

Published online by Cambridge University Press:  11 February 2009

Masanobu Taniguchi  and
Madan L. Puri
Masanobu Taniguchi
Affiliation:
Osaka University
Madan L. Puri
Affiliation:
Indiana University
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Abstract

Consider a linear regression model y1 = x1β + u1, where the u1'S afe weakly dependent random variables, the x1's are known design nonrandom variables, and β is an unknown parameter. We define an M-estimator βn of) β corresponding to a smooth score function. Then, the second-order Edgeworth expansion for βn is derived. Here we do not assume the normality of (u1), and (u1) includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(βn) of βn. Then, a sufficient condition for T to extinguish the second-order terms is given. The results are applicable to many statistical problems.

Information

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 2 , June 1996 , pp. 331 - 346
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

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. & Rao, R.R. (1976) Normal Approximation and Asymptotic Expansions. New York: Wiley.Google Scholar
Bose, A. (1988) Edgeworth correction by bootstrap in autoregressions. Annals of Statistics 4, 1709–1722.Google Scholar
Brillinger, D.R. (1975) Time Series: Data Analysis and Theory. New York: Holden-Day.Google Scholar
Chibisov, D.M. (1972) An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion. Theory of Probability and Its Applications 17, 620–630.CrossRefGoogle Scholar
Cotze, F. & Hipp, C. (1983) Asymptotic expansions for sums of weakly dependent random vectors. Zeitschrift fur Wahrscheinlickheits Theorie und Verwandte Gebiete 64, 211–239.Google Scholar
Hannan, E.J. (1970) Multiple Time Series. New York: Wiley.CrossRefGoogle Scholar
Lahiri, S.N. (1992) Bootstrapping M-estimators of a multiple linear regression parameter. Annals of Statistics 20, 1548–1570.CrossRefGoogle Scholar
Navidi, W. (1989) Edgeworth expansions for bootstrapping regression models. Annals of Statistics 17, 1472–1478.CrossRefGoogle Scholar
Qumsiyeh, M.B. (1990) Edgeworth expansion in regression models. Journal of Multivariate Analysis 35, 86–101.CrossRefGoogle Scholar
Ringland, J.T. (1983) Robust multiple comparisons. Journal of the American Statistical Association 78, 145–151.CrossRefGoogle Scholar
Taniguchi, M. (1987) Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes. Journal of Multivariate Analysis 21, 1–28.CrossRefGoogle Scholar
Taniguchi, M. (1991) Higher Order Asymptotic Theory for Time Series Analysis. Lecture Notes in Statistics, vol. 68. Heidelberg: Springer-Verlag.Google Scholar