Asymptotic theorems for kernel U-quantiles
About: This article is published in Electronic Journal of Statistics. The article was published on 01 Jan 2012. and is currently open access. The article focuses on the topics: Asymptotic analysis & Variable kernel density estimation.
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References
Nonparametric Statistical Data Modeling
TL;DR: An approach to statistical data analysis which is simultaneously parametric and nonparametric is described, and density-quantile functions, autoregressive density estimation, estimation of location and scale parameters by regression analysis of the sample quantile function, and quantile-box plots are introduced.
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A Smooth Nonparametric Estimator of a Quantile Function
TL;DR: In this article, a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile functions is proposed, which is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sampling quantile.
166
Relative Deficiency of Kernel Type Estimators of Quantiles
TL;DR: In this article, the asymptotic relative deficiency of the sample $q$-quantile with respect to kernel type estimators of the $ q$ -quantile is evaluated, based on the mean square errors of the estimators.
Asymptotic Normality of the Kernel Quantile Estimator
TL;DR: In this paper, the multidimensional asymptotic normality of the kernel quantile estimator is established under fairly general conditions on the underlying distribution function and on the kernel.
•Journal Article
The almost sure invariance principle for the empirical process of U-statistic structure
TL;DR: In this paper, a generalization of Kiefer's almost sure invariance principle for the empirical distribution function to empirical processes of a certain class of dependent random variables having a U-statistic structure with non-degenerate kernel is presented.
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