The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data

2021 ◽  
Vol 181 ◽  
pp. 104673
Author(s):  
Mustapha Mohammedi ◽  
Salim Bouzebda ◽  
Ali Laksaci
Keyword(s):  
Asymptotic Normality ◽  
Functional Data ◽  
Regression Estimator ◽  
Expectile Regression ◽  
Consistency And Asymptotic Normality ◽  
Kernel Type

scholarly journals PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS

2011 ◽  
Vol 27 (6) ◽  
pp. 1236-1278 ◽  
Author(s):  
Mika Meitz ◽  
Pentti Saikkonen
Keyword(s):  
Asymptotic Normality ◽  
Autoregressive Models ◽  
Garch Models ◽  
Martingale Difference ◽  
First Order ◽  
First Results ◽  
Consistency And Asymptotic Normality ◽  
Quasi Maximum Likelihood ◽  
Nonlinear Autoregressive ◽  
Nonlinear Autoregressive Models

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

scholarly journals NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA

2002 ◽  
Vol 18 (2) ◽  
pp. 420-468 ◽  
Author(s):  
Oliver Linton ◽  
Yoon-Jae Whang
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Asymptotic Normality ◽  
Nonparametric Estimation ◽  
Regression Function ◽  
Rates Of Convergence ◽  
Monte Carlo Experiment ◽  
Aggregated Data ◽  
Practical Performance ◽  
Consistency And Asymptotic Normality

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

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