论文信息 - On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models

On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models

This paper considers the multiple linear regression modelYi=xi?s+?i,i=i, ?, n, wherexi's are knownp×1 vectors,sis ap×1 vector of parameters, and?1,?2, ? are stationary, strongly mixing random variables. Letsndenote anM-estimator ofscorresponding to some score function?. Under some conditions on?,xi's and?i's, a two-term Edgeworth expansion for Studentized multivariateM-estimator is proved. Furthermore, it is shown that the moving block bootstrap is second-order correct for some suitable bootstrap analog of Studentizedsn.

Soumendra N. Lahiri | S. Lahiri

[1] G. Shorack. Bootstrapping robust regression , 1982 .

[2] J. Ghosh,et al. ON THE VALIDITY OF THE FORMAL EDGEWORTH EXPANSION , 1978 .

[3] K. Singh,et al. On the Asymptotic Accuracy of Efron's Bootstrap , 1981 .

[4] S. Nagaev,et al. Probability inequalities for sums of independent random variables with values in a Banach space , 1971 .

[5] John Haigh,et al. Normal Approximations and Asymptotic Expansions , 1977 .

[6] M. Tiro. Edgeworth expansion and bootstrap approximation for M-estimators of linear regression parameters with increasing dimensions , 1991 .

[7] S. Lahiri. Bootstrapping $M$-Estimators of a Multiple Linear Regression Parameter , 1992 .

[8] F. Götze. Approximations for multivariate U —statistics , 1987 .

[9] M. Qumsiyeh. Bootstrapping and empirical edgeworth expansions in multiple linear regression models , 1994 .

[10] D. Freedman. Bootstrapping Regression Models , 1981 .

[11] F. Götze,et al. The Edgeworth Expansion for $U$-Statistics of Degree Two , 1986 .

[12] B. Efron. Bootstrap Methods: Another Look at the Jackknife , 1979 .

[13] Soumendra N. Lahiri,et al. Second order optimality of stationary bootstrap , 1991 .

[14] H. Künsch. The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[15] Friedrich Götze,et al. Asymptotic expansions for sums of weakly dependent random vectors , 1983 .