# ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR OF REGRESSION FUNCTION UNDER NA ASSUMPTIONS

Liang, Han-Ying;Qi, Yan-Yan

• Published : 2007.05.31
• 54 4

#### Abstract

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

#### Keywords

regression function;NA error;wavelet estimator;asymptotic normality

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