scholarly journals Strong consistency of regression function estimator with martingale difference errors

2021 ◽  
Vol 19 (1) ◽  
pp. 1056-1068
Author(s):  
Yingxia Chen
Keyword(s):  
Strong Convergence ◽  
Regression Model ◽  
Unknown Function ◽  
Strong Consistency ◽  
Regression Function ◽  
Martingale Difference ◽  
Nonparametric Estimator ◽  
Convergence Properties ◽  
Fixed Design

Abstract In this paper, we consider the regression model with fixed design: Y i = g ( x i ) + ε i {Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i} , 1 ≤ i ≤ n 1\le i\le n , where { x i } \left\{{x}_{i}\right\} are the nonrandom design points, and { ε i } \left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and g g is an unknown function. Nonparametric estimator g n ( x ) {g}_{n}\left(x) of g ( x ) g\left(x) will be introduced and its strong convergence properties are established.

Spline Estimate of Nonparametric Regression Function under Martingale Difference Errors

2011 ◽  
Vol 403-408 ◽  
pp. 5239-5243
Author(s):  
Xin Qian Wu ◽  
Wan Cai Yang
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Kernel Method ◽  
Regression Function ◽  
Foreign Exchange Rate ◽  
Martingale Difference ◽  
Spline Method ◽  
Mild Conditions ◽  
Global Rate ◽  
Fixed Design

Nonparametric regression models with fixed design points and martingale difference errors are considered in this paper. Under mild conditions, optimal global rate of convergence of regression function estimator based on polynomial spline is obtained. Simulation results show that spline method outperforms kernel method at some cases. The regression function is fitted for the CNY/EUR foreign exchange rate series.

scholarly journals The Strong Consistency of the Estimator of Fixed-Design Regression Model under Negatively Dependent Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xuejun Wang ◽  
Meimei Ge ◽  
Shuhe Hu ◽  
Xize Wang
Keyword(s):  
Regression Model ◽  
Strong Consistency ◽  
Nearest Neighbor ◽  
Type Inequality ◽  
Fixed Design ◽  
Rosenthal Type Inequality ◽  
Fixed Design Regression

We study the strong consistency of estimator of fixed design regression model under negatively dependent sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the strong consistency for the nearest neighbor estimator is obtained.

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.

EXPONENTIALLY STRONG CONVERGENCE OF NON-CLASSICAL MULTIDIMENSIONAL CONTINUED FRACTION ALGORITHMS

2002 ◽  
Vol 02 (04) ◽  
pp. 563-586
Author(s):  
KENTARO NAKAISHI
Keyword(s):  
Strong Convergence ◽  
Continued Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Deterministic Case ◽  
Convergence Properties ◽  
Almost Everywhere ◽  
Multidimensional Continued Fraction

Convergence properties of multidimensional continued fraction algorithms introduced by V. Baladi and A. Nogueira are studied. The paper contains an arithmetic proof of almost everywhere exponentially strong convergence of some two-dimensional Markovian random algorithms and dynamically defined ones. A special three-dimensional deterministic case is also discussed.

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