scholarly journals On the Convergence Rate for a Kernel Estimate of the Regression Function

2016 ◽  
Vol 5 (2) ◽  
pp. 29
Author(s):  
Mounir ARFI
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Kernel Estimator ◽  
Regression Function ◽  
Kernel Estimate ◽  
Compact Sets

We give the rate of the uniform convergence for the kernel estimate of the regression function over a sequence of compact sets which increases to $\mathbb{R}^{d}$ when $n$ approaches the infinity and when the observed process is $\varphi$-mixing. The used estimator for the regression function is the kernel estimator proposed by Nadaraya, Watson (1964).

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 Mazur's intersection property of balls for compact convex sets

1987 ◽  
Vol 35 (2) ◽  
pp. 267-274 ◽  
Author(s):  
J. H. M. Whitfield ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Uniform Convergence ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Intersection Property ◽  
Compact Sets ◽  
Compact Convex Set ◽  
Mazur's Intersection Property

We show that every compact convex set in a Banach space X is an intersection of balls provided the cone generated by the set of all extreme points of the dual unit ball of X* is dense in X* in the topology of uniform convergence on compact sets in X. This allows us to renorm every Banach space with transfinite Schauder basis by a norm which shares the mentioned intersection property.

scholarly journals Convergence Rate of Extremes for the General Error Distribution

2010 ◽  
Vol 47 (3) ◽  
pp. 668-679 ◽  
Author(s):  
Zuoxiang Peng ◽  
Saralees Nadarajah ◽  
Fuming Lin
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Random Sequence ◽  
Extreme Value ◽  
Error Distribution ◽  
Distribution Of The Maximum ◽  
Uniform Convergence Rate ◽  
Independent Identically Distributed ◽  
General Error

Let {Xn, n ≥ 1} be an independent, identically distributed random sequence with each Xn having the general error distribution. In this paper we derive the exact uniform convergence rate of the distribution of the maximum to its extreme value limit.

NONPARAMETRIC COINTEGRATING REGRESSION WITH NNH ERRORS

2012 ◽  
Vol 29 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Qiying Wang ◽  
Ying Xiang Rachel Wang
Keyword(s):  
Regression Model ◽  
Generating Function ◽  
Regression Function ◽  
Kernel Estimate ◽  
Uniform Consistency

This paper studies a nonlinear cointegrating regression model with nonlinear nonstationary heteroskedastic error processes. We establish uniform consistency for the conventional kernel estimate of the unknown regression function and develop atwo-stage approach for the estimation of the heterogeneity generating function.

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