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| Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples |
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Citation： |
Hongchang HU,Li WU.Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples[J].Chinese Annals of Mathematics B,2012,33(4):609~624 |
| Page view： 1902
Net amount： 1255 |
Authors： |
Hongchang HU; Li WU; |
Foundation： |
the National Natural Science Foundation of China (No. 11071022), the Key Project of the Ministry of Education of China (No. 209078) and the Youth Project of Hubei Provincial Department of Education of China (No. Q20122202). |
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| Abstract： |
Consider the following heteroscedastic semiparametric regression model:
$$ y_i=X^{\rm T}_i\beta+g(t_i)+\sigma_ie_i,\quad 1\leq i\leq n, $$
where $\{X_i,\,\,1\leq i\leq n\}$ are random design points, errors $\{e_i,\,\,1\leq i\leq n\}$ are negatively associated (NA) random variables, $\sigma^2_i=h(u_i)$, and $\{u_i\}$ and $\{t_i\}$ are two nonrandom sequences on $[0,1]$. Some wavelet estimators of the parametric component $\beta$, the nonparametric component $g(t)$ and the variance function $h(u)$ are given. Under some general conditions,the strong convergence rate of these wavelet estimators is $O(n^{-\frac{1}{3}}\log n)$. Hence our results are extensions of those results on independent random error settings. |
Keywords： |
Semiparametric regression model, Wavelet estimate, Negatively associated random error, Strong convergence rate |
Classification： |
62G05, 62G20 |
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