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

作者：Liang Hanying^*

来源：Journal of Systems Science and Complexity, 2011, 24(4): 725-737.

DOI：10.1007/s11424-010-8354-8

• alpha-mixing
• asymptotic normality
• heteroscedastic regression model
• wavelet estimator

Consider heteroscedastic regression model Y (ni) = g(x (ni) ) + sigma (ni) E > (ni) (1 a parts per thousand currency sign i a parts per thousand currency sign n), where sigma (ni) (2) = f(u (ni) ), the design points (x (ni) , u (ni) ) are known and nonrandom, g(center dot) and f(center dot) are unknown functions defined on closed interval [0, 1], and the random errors {E > (ni) , 1 a parts per thousand currency sign i a parts per thousand currency sign n} are assumed to have the same distribution as {xi (i) , 1 a parts per thousand currency sign i a parts per thousand currency sign n}, which is a stationary and alpha-mixing time series with E xi (i) = 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(center dot) and f(center dot). Finite sample behavior of the estimators is investigated via simulations, too.

• 出版日期2011-8
• 单位同济大学