Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors
Consider the semiparametric regression model yi=xi[beta]+g(ti)+Vi,1<=i<=n, where [beta] is an unknown parameter of interest, (xi,ti) are nonrandom design points, yi are the response variables, g([dot operator]) is an unknown function defined on the closed interval [0,1], and the correlated errors , with , and ei are negatively associated random variables. Under appropriate conditions, in this paper, we derive Berry-Esseen type bounds for estimators of [beta] and g([dot operator]). As a corollary, by making a certain choice of the weights, we give the Berry-Esseen type bounds for estimators of [beta] and g([dot operator]); they are O(n-1/4(logn)3/4) and O(n-3/28(logn)9/28), respectively, and under further restriction for the weights, the Berry-Esseen type bound for estimator of g([dot operator]) can also attain O(n-1/4(logn)3/4).
Year of publication: |
2009
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Authors: | Liang, Han-Ying ; Fan, Guo-Liang |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 100.2009, 1, p. 1-15
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Publisher: |
Elsevier |
Keywords: | 62G08 Semiparametric model Negatively associated Berry-Esseen type bound Linear process error |
Saved in:
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