some asymptotic results of kernel density estimator in length-biased sampling
Authors
abstract
in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data.
similar resources
Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...
full textA Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...
full textAsymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data
Kernel density estimators are the basic tools for density estimation in non-parametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paper, we initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...
full texta berry-esseen type bound for the kernel density estimator of length-biased data
length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...
full textasymptotic behaviors of nearest neighbor kernel density estimator in left-truncated data
kernel density estimators are the basic tools for density estimation in non-parametric statistics. the k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. in this paper, we initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...
full textAsymptotic 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.
full textMy Resources
Save resource for easier access later
Journal title:
journal of sciences, islamic republic of iranPublisher: university of tehran
ISSN 1016-1104
volume 24
issue 1 2013
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023