Abstract
Consider the semiparametric regression model Yi = xi b +g (ti) + ei, i= 1, ..., n, where the linear process errors ei = � ∞=−∞ ajei−j with � ∞=−∞ � a j � < ∞ , and {ei} are identically distributed and strong mixing innovations with zero mean. Under appropriate conditions, the Berry-Esseen type bounds of wavelet estimators for b and g(·) are established. Our results obtained generalize the results of nonparametric regression model by Li et al. to semiparametric regression model. Mathematical Subject Classification: 62G05; 62G08.
Highlights
Regression analysis is one of the most mature and widely applied branches of statistics
Semiparametric regressions have received more and more attention. This is mainly because semiparametric regression reduces the high risk of misspecification relating to a fully parametric model and avoids some serious drawbacks of fully nonparametric methods
We study the Berry-Esseen type bounds for wavelet estimators of b and g(·) in model (1.1) based linear process errors {εi} satisfying the following basic assumption (A1)
Summary
Regression analysis is one of the most mature and widely applied branches of statistics. We study the Berry-Esseen type bounds for wavelet estimators of b and g(·) in model (1.1) based linear process errors {εi} satisfying the following basic assumption (A1). N), lim sup √ l n→∞ n log n max 1≤m≤n m uji i=1 After these assumptions and notations we can formulate the main results as follows: Theorem 2.1.
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