On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

ar X iv : 1 40 9 . 00 55 v 1 [ m at h . ST ] 2 9 A ug 2 01 4 On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

Abstract. Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result nonp...

Asymptotic normality of Powell’s kernel estimator

In this paper, we establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator.

Consistency and asymptotic normality of the maximum likelihood estimator in a zero-inflated generalized Poisson regression

Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zeroinflation occur. We study in this paper regression models based on the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by McCull...

Asymptotic Normality of Wavelet Estimator of Regression Function under Na Assumptions

Consider the heteroscedastic regression model Yi = g(xi) + σi2i (1 ≤ i ≤ n), where σ2 i = f(ui), the design points (xi, ui) are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors 2i 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.

Asymptotic normality of randomly truncated stochastic algorithms