Asymptotic normality of wavelet estimator in heteroscedastic model with α-mixing errors

Consider heteroscedastic regression model Yni = g(xni) + σniɛni (1 ≤ i ≤ n), where σni2 = f(uni), the design points (xni, uni) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛni, 1 ≤ i ≤ n} are assumed to have the same distribution as {ξi, 1 ≤ i ≤ n}, which is a stationary and α-mixing time series with Eξi = 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too.

[1]  L. Xue STRONG UNIFORM CONVERBENCE RATES OF WAVELET ESTIMATES OF REGRESSION FUNCTION UNDER COMPLETE AND CENSORED DATA , 2002 .

[2]  A. Georgiev Consistent nonparametric multiple regression: the fixed design case , 1988 .

[3]  Peter Hall,et al.  On wavelet methods for estimating smooth functions , 1995 .

[4]  P. Doukhan Mixing: Properties and Examples , 1994 .

[5]  Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model , 1999 .

[6]  George G. Roussas,et al.  Fixed design regression for time series: asymptotic normality , 1992 .

[7]  G. Walter Wavelets and other orthogonal systems with applications , 1994 .

[8]  I. Johnstone,et al.  Density estimation by wavelet thresholding , 1996 .

[9]  V. Volkonskii,et al.  Some Limit Theorems for Random Functions. II , 1959 .

[10]  Xian Zhou,et al.  Wavelet estimation in varying-coefficient partially linear regression models , 2004 .

[11]  HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS , 2002 .

[12]  Han-Ying Liang,et al.  Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences , 2005 .

[13]  Han-Ying Liang,et al.  ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR OF REGRESSION FUNCTION UNDER NA ASSUMPTIONS , 2007 .

[14]  L. Han-ying,et al.  Wavelet estimation in nonparametric model under martingale difference errors , 2004 .

[15]  George G. Roussas,et al.  Consistent regression estimation with fixed design points under dependence conditions , 1989 .

[16]  A. Antoniadis,et al.  Wavelet Methods for Curve Estimation , 1994 .

[17]  Wavelet Estimation in Heteroscedastic Model Under Censored Samples , 2007 .

[18]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[19]  Shanchao Yang,et al.  Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application , 2007 .