Bulletin of the
Korean Mathematical Society BKMS

Consider the heteroscedastic regression model $Y_i=g(x_i)+\sigma_i \epsilon_i$ ($1 \le i\le n)$, where $\sigma_i^2=f(u_i)$, 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

MSC numbers: 62G05