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http://dx.doi.org/10.4134/BKMS.2007.44.2.247

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR OF REGRESSION FUNCTION UNDER NA ASSUMPTIONS  

Liang, Han-Ying (DEPARTMENT OF MATHEMATICS TONGIL UNIVERSITY)
Qi, Yan-Yan (DEPARTMENT OF MATHEMATICS TONGIL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.44, no.2, 2007 , pp. 247-257 More about this Journal
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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