Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

Sankhya A ◽  
2011 ◽  
Vol 73 (1) ◽  
pp. 125-141 ◽  
Author(s):  
Ali Laksaci ◽  
Mohamed Lemdani ◽  
Elias Ould Saïd
Keyword(s):  
Kernel Estimator ◽  
Dependent Data ◽  
Asymptotic Results ◽  
Conditional Quantile

Asymptotic for LS estimators in the EV regression model for dependent errors

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4845-4856
Author(s):  
Konrad Furmańczyk
Keyword(s):  
Regression Model ◽  
Functional Dependence ◽  
Dependent Data ◽  
Errors In Variables ◽  
Mixing Conditions ◽  
Asymptotic Results ◽  
Dependence Measure ◽  
Wide Range ◽  
Ev Regression Model ◽  
Linear And Nonlinear

We study consistency and asymptotic normality of LS estimators in the EV (errors in variables) regression model under weak dependent errors that involve a wide range of linear and nonlinear time series. In our investigations we use a functional dependence measure of Wu [16]. Our results without mixing conditions complete the known asymptotic results for independent and dependent data obtained by Miao et al. [7]-[10].

scholarly journals KERNEL ESTIMATION WHEN DENSITY MAY NOT EXIST

2008 ◽  
Vol 24 (3) ◽  
pp. 696-725 ◽  
Author(s):  
Victoria Zinde-Walsh
Keyword(s):  
Empirical Studies ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Generalized Functions ◽  
Continuous Variables ◽  
Asymptotic Results ◽  
Absolutely Continuous ◽  
Conditional Mean ◽  
Special Cases ◽  
Nonparametric Kernel

Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and explanations are discussed in the paper. Generally, any distribution function consists of absolutely continuous, discrete, and singular components, but only a few special cases of nonparametric estimation involving singularity have been examined in the literature, and asymptotic theory under the general setup has not been developed. In this paper the asymptotic process for the kernel estimator is examined by means of the generalized functions and generalized random processes approach; it provides a unified theory because density and its derivatives can be defined as generalized functions for any distribution, including cases with singular components. The limit process for the kernel estimator of density is fully characterized in terms of a generalized Gaussian process. Asymptotic results for the Nadaraya–Watson conditional mean estimator are also provided.

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