scholarly journals A Note on the Adaptive Estimation of a Multiplicative Separable Regression Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Christophe Chesneau
Keyword(s):  
Regression Model ◽  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Adaptive Estimation ◽  
Regression Function ◽  
Nonparametric Regression Model ◽  
Mean Integrated Squared Error ◽  
Squared Error ◽  
Integrated Squared Error ◽  
Separable Regression

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.

scholarly journals Estimasi Fungsi Regresi Dalam Model Regresi Nonparametrik Birespon Menggunakan Estimator Smoothing Spline dan Estimator Kernel

2018 ◽  
Vol 15 (2) ◽  
pp. 20 ◽  
Author(s):  
Budi Lestari
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Kernel Estimator ◽  
Regression Function ◽  
Predictor Variables ◽  
Smoothing Spline ◽  
Estimating Functions ◽  
Nonparametric Regression Model ◽  
Estimation Techniques ◽  
Connection Pattern

Abstract Regression model of bi-respond nonparametric is a regression model which is illustrating of the connection pattern between respond variable and one or more predictor variables, where between first respond and second respond have correlation each other. In this paper, we discuss the estimating functions of regression in regression model of bi-respond nonparametric by using different two estimation techniques, namely, smoothing spline and kernel. This study showed that for using smoothing spline and kernel, the estimator function of regression which has been obtained in observation is a regression linier. In addition, both estimators that are obtained from those two techniques are systematically only different on smoothing matrices. Keywords: kernel estimator, smoothing spline estimator, regression function, bi-respond nonparametric regression model. AbstrakModel regresi nonparametrik birespon adalah suatu model regresi yang menggambarkan pola hubungan antara dua variabel respon dan satu atau beberapa variabel prediktor dimana antara respon pertama dan respon kedua berkorelasi. Dalam makalah ini dibahas estimasi fungsi regresi dalam  model regresi nonparametrik birespon menggunakan dua teknik estimasi yang berbeda, yaitu smoothing spline dan kernel. Hasil studi ini menunjukkan bahwa, baik menggunakan smoothing spline maupun menggunakan kernel, estimator fungsi regresi yang didapatkan merupakan fungsi linier dalam observasi. Selain itu, kedua estimator fungsi regresi yang didapatkan dari kedua teknik estimasi tersebut secara matematis hanya dibedakan oleh matriks penghalusnya.Kata Kunci : Estimator Kernel, Estimator Smoothing Spline, Fungsi Regresi, Model Regresi Nonparametrik Birespon.

scholarly journals Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

1990 ◽  
Vol 6 (4) ◽  
pp. 466-479 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Yoon-Jae Whang
Keyword(s):  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Regression Function ◽  
Curse Of Dimensionality ◽  
Finite Sample ◽  
Squared Error ◽  
Convergence Results ◽  
Additive Regression ◽  
Parametric Regression Models

This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between different regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully non-parametric regression models.In this paper, we present a finite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show that AIR models do circumvent the curse of dimensionality. A lower bound on the rate of convergence of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector. Series estimators with fixed and data-dependent truncation parameters are considered.

scholarly journals Lp-Adaptive Estimation Under Partially Linear Constraint in Regression Model

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.

scholarly journals A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Christophe Chesneau
Keyword(s):  
Regression Function ◽  
Rates Of Convergence ◽  
Nonparametric Regression Model ◽  
Random Design ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean ◽  
Derivatives Of ◽  
Wavelet Estimators ◽  
Fast Rates

We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions.

scholarly journals Bayesian bandwidth estimation for local linear fitting in nonparametric regression models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Han Lin Shang ◽  
Xibin Zhang
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Regression Function ◽  
Linear Estimator ◽  
Bandwidth Estimation ◽  
Nonparametric Regression Model ◽  
Mixture Density ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Error Density

AbstractThis paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by a location-mixture density of Gaussian densities with means the individual errors and variance a constant parameter. This mixture density has the form of a kernel density estimator of errors and is referred to as the kernel-form error density (c.f. Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34.). While (Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34) use the local constant (also known as the Nadaraya-Watson) estimator to estimate the regression function, we extend this to the local linear estimator, which produces more accurate estimation. The proposed investigation is motivated by the lack of data-driven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernel-form error density. Treating bandwidths as parameters, we derive an approximate (pseudo) likelihood and a posterior. A simulation study shows that the proposed bandwidth estimation outperforms the rule-of-thumb and cross-validation methods under the criterion of integrated squared errors. The proposed bandwidth estimation method is validated through a nonparametric regression model involving firm ownership concentration, and a model involving state-price density estimation.

scholarly journals Nonparametric relative recursive regression

2020 ◽  
Vol 8 (1) ◽  
pp. 221-238
Author(s):  
Yousri Slaoui ◽  
Salah Khardani
Keyword(s):  
Approximation Method ◽  
Regression Function ◽  
Mean Integrated Squared Error ◽  
Response Variable ◽  
Squared Error ◽  
Regression Estimators ◽  
Integrated Squared Error ◽  
The Mean ◽  
Outlier Data ◽  
Bias Variance

AbstractIn this paper, we propose the problem of estimating a regression function recursively based on the minimization of the Mean Squared Relative Error (MSRE), where outlier data are present and the response variable of the model is positive. We construct an alternative estimation of the regression function using a stochastic approximation method. The Bias, variance, and Mean Integrated Squared Error (MISE) are computed explicitly. The asymptotic normality of the proposed estimator is also proved. Moreover, we conduct a simulation to compare the performance of our proposed estimators with that of the two classical kernel regression estimators and then through a real Malaria dataset.

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