scholarly journals An oracle property of the Nadaraya–Watson kernel estimator for high‐dimensional nonparametric regression

2018 ◽  
Vol 46 (3) ◽  
pp. 735-764
Author(s):  
Daniel Conn ◽  
Gang Li
Keyword(s):  
Nonparametric Regression ◽  
Kernel Estimator ◽  
Oracle Property ◽  
High Dimensional

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.

Several Aspects of Nonparametric Prediction of Nonlinear Time Series

2019 ◽  
Vol 65 (1) ◽  
pp. 7-24
Author(s):  
Witold Orzeszko
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Kernel Smoothing ◽  
Kernel Estimator ◽  
Monte Carlo Study ◽  
Nonlinear Time Series ◽  
Fixed Number ◽  
Parametric Models ◽  
Parametric Approach ◽  
Local Linear

Nonparametric regression is an alternative to the parametric approach, which consists of applying parametric models, i.e. models of the certain functional form with a fixed number of parameters. As opposed to the parametric approach, nonparametric models have a general form, which can be approximated increasingly precisely when the sample size grows. Hereby they do not impose such restricted assumptions about the form of the modelling dependencies and in consequence, they are more flexible and let the data speak for themselves. That is why they are a promising tool for forecasting, especially in case of nonlinear time series. One of the most popular nonparametric regression method is the Nadaraya- Watson kernel smoothing. Nowadays, there are a number of variations of this method, like the local-linear kernel estimator, which combines the local linear approximation and the kernel estimator. In the paper a Monte Carlo study is conducted in order to assess the usefulness of the kernel smoothers to nonlinear time series forecasting and to compare them with the other techniques of forecasting.

scholarly journals Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dyah P. Rahmawati ◽  
I. N. Budiantara ◽  
Dedy D. Prastyo ◽  
Made A. D. Octavanny
Keyword(s):  
Nonparametric Regression ◽  
Kernel Estimator ◽  
Least Square ◽  
Spline Smoothing ◽  
Nonparametric Regression Model ◽  
Weighted Least Square ◽  
Proposed Model ◽  
Mixed Estimator ◽  
Stage Estimation ◽  
Poor Population

Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

LASSO-Type Variable Selection Methods for High-Dimensional Data

2013 ◽  
Vol 444-445 ◽  
pp. 604-609
Author(s):  
Guang Hui Fu ◽  
Pan Wang
Keyword(s):  
Variable Selection ◽  
High Dimensional Data ◽  
Real Data ◽  
Oracle Property ◽  
High Dimensional ◽  
Data Sets ◽  
Group Effect ◽  
Selection Methods ◽  
Variable Selection Method ◽  
Type Variable

LASSO is a very useful variable selection method for high-dimensional data , But it does not possess oracle property [Fan and Li, 200 and group effect [Zou and Hastie, 200. In this paper, we firstly review four improved LASSO-type methods which satisfy oracle property and (or) group effect, and then give another two new ones called WFEN and WFAEN. The performance on both the simulation and real data sets shows that WFEN and WFAEN are competitive with other LASSO-type methods.

GRID: A variable selection and structure discovery method for high dimensional nonparametric regression

2020 ◽  
Vol 48 (3) ◽  
pp. 1848-1874
Author(s):  
Francesco Giordano ◽  
Soumendra Nath Lahiri ◽  
Maria Lucia Parrella
Keyword(s):  
Variable Selection ◽  
Nonparametric Regression ◽  
High Dimensional ◽  
Discovery Method
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