Adaptive estimation for an inverse regression model with unknown operator

We investigate the estimation of a multiplicative separable regression function from a bidimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of convergence under the MISE over Besov balls.

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On Conditional Distribution of Sliced Inverse Regression Model

New Developments in Psychometrics ◽

10.1007/978-4-431-66996-8_39 ◽

2003 ◽

pp. 347-354

Author(s):

Masahiro Mizuta

Keyword(s):

Regression Model ◽

Conditional Distribution ◽

Sliced Inverse Regression ◽

Inverse Regression

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Adaptive Estimation in ARCH Models

Econometric Theory ◽

10.1017/s0266466600007970 ◽

1993 ◽

Vol 9 (4) ◽

pp. 539-569 ◽

Cited By ~ 87

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.

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Lp-Adaptive Estimation Under Partially Linear Constraint in Regression Model

Journal of Mathematics Research ◽

10.5539/jmr.v12n6p74 ◽

2020 ◽

Vol 12 (6) ◽

pp. 74

Author(s):

Kouame Florent Kouakou ◽

Armel Fabrice Evrard Yode

Keyword(s):

Regression Model ◽

Adaptive Estimation ◽

Linear Structure ◽

Regression Function ◽

Estimation Procedure ◽

Linear Constraint ◽

Nonparametric Regression Model ◽

Partially Linear ◽

Lp Norm ◽

Multivariate Estimation

We study the problem of multivariate estimation in the nonparametric regression model with random design. We assume that the regression function to be estimated possesses partially linear structure, where parametric and nonparametric components are both unknown. Based on Goldenshulger and Lepski methodology, we propose estimation procedure that adapts to the smoothness of the nonparametric component, by selecting from a family of specific kernel estimators. We establish a global oracle inequality (under the Lp-norm, 1≤p＜1) and examine its performance over the anisotropic H¨older space.

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