ESTIMATION OF COVARIANCE MATRIX BASED ON SPLINE ESTIMATOR IN HOMOSCEDASTIC MULTI-RESPONSES NONPARAMETRIC REGRESSION MODEL IN CASE OF UNBALANCE NUMBER OF OBSERVATIONS

In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.

Download Full-text

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 ◽

Nonparametric Regression ◽

Nonparametric Regression Model ◽

Arab States

Download Full-text

Estimation of nonstationary nonparametric regression model with multiplicative structure

Econometrics Journal ◽

10.1093/ectj/utab018 ◽

2021 ◽

Author(s):

Likai Chen ◽

Ekaterina Smetanina ◽

Wei Biao Wu

Keyword(s):

Regression Model ◽

Nonparametric Regression ◽

Risk Premium ◽

Convergence Rates ◽

Broad Class ◽

Estimation Procedure ◽

Small Samples ◽

Nonparametric Regression Model ◽

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.

Download Full-text

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 ◽

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.

Download Full-text