Estimation of nonstationary nonparametric regression model with multiplicative structure

Risk Premium ◽

Convergence Rates ◽

Broad Class ◽

Estimation Procedure ◽

Small Samples ◽

Conditional Mean ◽

Mean Function

Abstract This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth, and estimating the shape of the monthly risk premium for S&P 500 Index data.

Complete consistency for the estimator of nonparametric regression model based on m-END errors

Open Mathematics ◽

10.1515/math-2021-0081 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1197-1209

Author(s):

Shui-Li Zhang ◽

Tiantian Hou ◽

Cong Qu

Keyword(s):

Regression Model ◽

Convergence Rates ◽

Complete Consistency ◽

Model Based ◽

General Conditions

Abstract In this paper, we study the complete consistency for the estimator of nonparametric regression model based on m-END errors and obtain the convergence rates of the complete consistency under more general conditions. Finally, some simulations are illustrated to verify the validity of our results.

On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise

Mathematica Slovaca ◽

10.1515/ms-2017-0324 ◽

2019 ◽

Vol 69 (6) ◽

pp. 1485-1500 ◽

Cited By ~ 2

Author(s):

Yuncai Yu ◽

Xinsheng Liu ◽

Ling Liu ◽

Weisi Liu

Keyword(s):

Regression Model ◽

Numerical Simulations ◽

Besov Spaces ◽

Convergence Rates ◽

Wavelet Thresholding ◽

Optimal Convergence ◽

Optimal Convergence Rates ◽

Block Thresholding

Abstract This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.

Nonparametric regression model of autocorrelation problem in the general budget of Arab States through (2008-2020)

Journal of Statistics and Management Systems ◽

10.1080/09720510.2020.1859807 ◽

2021 ◽

pp. 1-9

Author(s):

Duraid Hussein Badr

Keyword(s):

Regression Model ◽

Arab States

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

Jurnal Matematika Statistika dan Komputasi ◽

10.20956/jmsk.v15i2.5710 ◽

2018 ◽

Vol 15 (2) ◽

pp. 20 ◽

Cited By ~ 5

Author(s):

Budi Lestari

Keyword(s):

Regression Model ◽

Kernel Estimator ◽

Regression Function ◽

Predictor Variables ◽

Smoothing Spline ◽

Estimating Functions ◽

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.