scholarly journals A Note on the Adaptive Estimation of a Conditional Continuous-Discrete Multivariate Density by Wavelet Methods

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Christophe Chesneau ◽  
Hassan Doosti
Keyword(s):  
Simulation Study ◽  
Wide Class ◽  
Adaptive Estimation ◽  
Rates Of Convergence ◽  
Conditional Density ◽  
Adaptive Estimator ◽  
Practical Performance ◽  
Multivariate Density ◽  
Wavelet Methods ◽  
Theoretical Performance

We investigate the estimation of a multivariate continuous-discrete conditional density. We develop an adaptive estimator based on wavelet methods. We prove its good theoretical performance by determining sharp rates of convergence under the Lp risk with p≥1 for a wide class of unknown conditional densities. A simulation study illustrates the good practical performance of our estimator.

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.

scholarly journals ADAPTIVE ESTIMATION OF FUNCTIONALS IN NONPARAMETRIC INSTRUMENTAL REGRESSION

2015 ◽  
Vol 32 (3) ◽  
pp. 612-654 ◽  
Author(s):  
Christoph Breunig ◽  
Jan Johannes
Keyword(s):  
Rate Of Convergence ◽  
Adaptive Estimation ◽  
Optimal Choice ◽  
Optimal Rate ◽  
Structural Function ◽  
Regularity Conditions ◽  
Adaptive Estimator ◽  
Optimal Rate Of Convergence ◽  
Pointwise Estimation ◽  
Additional Regularity

We consider the problem of estimating the valueℓ(ϕ) of a linear functional, where the structural functionϕmodels a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based on a dimension reduction technique and additional thresholding. It is shown that this estimator is consistent and can attain the minimax optimal rate of convergence under additional regularity conditions. This, however, requires an optimal choice of the dimension parametermdepending on certain characteristics of the structural functionϕand the joint distribution of the regressor and the instrument, which are unknown in practice. We propose a fully data driven choice ofmwhich combines model selection and Lepski’s method. We show that the adaptive estimator attains the optimal rate of convergence up to a logarithmic factor. The theory in this paper is illustrated by considering classical smoothness assumptions and we discuss examples such as pointwise estimation or estimation of averages of the structural functionϕ.

scholarly journals BLOCK THRESHOLDING FOR A DENSITY ESTIMATION PROBLEM WITH A CHANGE-POINT

2009 ◽  
Vol 02 (04) ◽  
pp. 545-555 ◽  
Author(s):  
Christophe Chesneau
Keyword(s):  
Density Estimation ◽  
Change Point ◽  
General Framework ◽  
Rates Of Convergence ◽  
Estimation Problem ◽  
Adaptive Estimator ◽  
Function Classes ◽  
Wide Range ◽  
Optimal Rates Of Convergence ◽  
Block Thresholding

We consider a density estimation problem with a change-point. The contribution of the paper is theoretical: we develop an adaptive estimator based on wavelet block thresholding and we evaluate these performances via the minimax approach under the 𝕃p risk with p ≥ 1 over a wide range of function classes: the Besov classes, [Formula: see text] (with no particular restriction on the parameters π and r). Under this general framework, we prove that it attains near optimal rates of convergence.

scholarly journals Adaptive Estimation in ARCH Models

1993 ◽  
Vol 9 (4) ◽  
pp. 539-569 ◽  
Author(s):  
Oliver Linton
Keyword(s):  
Regression Model ◽  
Functional Form ◽  
Adaptive Estimation ◽  
Conditional Density ◽  
Arch Models ◽  
Error Density ◽  
The Mean

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly identifiable with the error density. We consider a reparameterization of the variance process and show that the identifiable parameters of this process are adaptively estimable.

scholarly journals A note on the adaptive estimation of the differential entropy by wavelet methods

2017 ◽  
Vol 58 (1) ◽  
pp. 87-100 ◽  
Author(s):  
 Chesneau Christophe ◽  
Navarro Fabien ◽  
Serea Oana Silvia
Keyword(s):  
Adaptive Estimation ◽  
Differential Entropy ◽  
Wavelet Methods

Adaptive Estimation of a Conditional Density

2015 ◽  
Vol 84 (2) ◽  
pp. 291-316 ◽  
Author(s):  
Ann-Kathrin Bott ◽  
Michael Kohler
Keyword(s):  
Adaptive Estimation ◽  
Conditional Density

Semiparametric efficient adaptive estimation of the GJR-GARCH model

2018 ◽  
Vol 35 (3-4) ◽  
pp. 141-160
Author(s):  
Nicola Ciccarelli
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Adaptive Estimation ◽  
Conditional Variance ◽  
Likelihood Estimator ◽  
Adaptive Estimator ◽  
Asymptotically Normal ◽  
Semiparametric Estimator ◽  
Quasi Maximum Likelihood

Abstract In this paper we derive a semiparametric efficient adaptive estimator for the GJR-GARCH {(1,1)} model. We first show that the quasi-maximum likelihood estimator is consistent and asymptotically normal for the model used in analysis, and we secondly derive a semiparametric estimator that is more efficient than the quasi-maximum likelihood estimator. Through Monte Carlo simulations, we show that the semiparametric estimator is adaptive for the parameters included in the conditional variance of the GJR-GARCH {(1,1)} model with respect to the unknown distribution of the innovation.

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