Legendre wavelet approximation of functions having derivatives of Lipschitz class

In this paper, Legendre Wavelet approximation of functions f having first derivative f' and second derivative f'' of Lip? class, 0 < ? ? 1, have been determined. These wavelet estimators are sharper, better and best possible in Wavelet Analysis. It is observed that the LegendreWavelet estimator of f whose f'' ? Lip? is sharper than the estimator of f having f ' ?Lip? class.

Wavelet regression estimation over Lp risk based on negatively associated sample

This paper considers wavelet estimations of a regression function based on negatively associated sample. We provide upper bound estimations over [Formula: see text] risk of linear and nonlinear wavelet estimators in Besov space, respectively. When the random sample reduces to the independent case, our convergence rates coincide with the optimal convergence rates of classical nonparametric regression estimation.

A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors

In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.

Asymptotic properties of wavelet estimators in heteroscedastic semiparametric model based on negatively associated innovations

Consider the heteroscedastic semiparametric regression model $y_{i}=x_{i}\beta+g(t_{i})+\varepsilon_{i}$yi=xiβ+g(ti)+εi, $i=1, 2, \ldots, n$i=1,2,…,n, where β is an unknown slope parameter, $\varepsilon_{i}=\sigma_{i}e_{i}$εi=σiei, $\sigma^{2}_{i}=f(u_{i})$σi2=f(ui), $(x_{i},t_{i},u_{i})$(xi,ti,ui) are nonrandom design points, $y_{i}$yi are the response variables, f and g are unknown functions defined on the closed interval $[0,1]$[0,1], random errors $\{e_{i} \}${ei} are negatively associated (NA) random variables with zero means. Whereas kernel estimators of β, g, and f have attracted a lot of attention in the literature, in this paper, we investigate their wavelet estimators and derive the strong consistency of these estimators under NA error assumption. At the same time, we also obtain the Berry–Esséen type bounds of the wavelet estimators of β and g.

Berry-Esseen bounds for wavelet estimator in time-varying coefficient models with censored dependent data

In this paper, we discuss wavelet estimation of time-varying coefficient models based on censored data where the survival and the censoring times are from a stationary α-mixing sequence. Under the appropriate conditions, the Berry-Esseen bouds of wavelet estimators are established. For the purpose of statistical inference, a random weighted wavelet estimator of the time-varying coefficient is also constructed, and some approximation rates are given.