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.

Nonlinear wavelet shrinkage estimator of nonparametric regularity regression function via cross-validation with simulation study

2017 ◽  
Vol 15 (06) ◽  
pp. 1750057
Author(s):  
Mahmoud Afshari
Keyword(s):  
Simulation Study ◽  
Cross Validation ◽  
Kernel Estimator ◽  
Regression Function ◽  
Data Sets ◽  
Wavelet Shrinkage ◽  
Wavelet Theory ◽  
New Techniques ◽  
One Dimensional ◽  
Regression Techniques

Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using [Formula: see text] software to compare purpose estimator with another estimators.

scholarly journals تقدير دالة الأنحدار اللامعلمي باستخدام بعض الطرائق اللامعلمية الرتيبة

2008 ◽  
Vol 14 (50) ◽  
pp. 304
Author(s):  
ياسمين عبد الرحمن محمد ◽  
دجلة ابراهيم مهدي
Keyword(s):  
Mean Square Error ◽  
Monotone Function ◽  
Minimum Mean Square Error ◽  
Kernel Estimator ◽  
Regression Function ◽  
Least Square ◽  
Maximum Efficiency ◽  
Mean Square ◽  
Statistical Measures ◽  
Monotone Methods

This research was concerning to study monotone nonparametric methods for estimating the nonparametric regression function (i.e treatment outlier) to achieve a monotone function (increasing or decreasing). So we will use the monotone methods to treatment outlier but after estimate the regression function with use kernel estimator (Nadarya - Watson) these methods are:- 1- Mukerjee method takes averages of maximums and minimum of subsets of the data was used to adjust the initial kernel regression estimates and use the researcher special case when . 2- Algorithm least square isotonic regression. In the experimental aspect comparison was done of which is the best methods through the simulation procedure using Mote Carlo method using five models. While in the application aspect practical application was done on data represent the measurements for blood pressure patients. In both aspects we use two of the important statistical measures which are Mean square error (MSE) and efficiency. We find through the application that the best method is Mukerjee method for general case as it has minimum Mean square error and maximum efficiency.  

scholarly journals Asymptotic normality of the relative error regression function estimator for censored and time series data

2021 ◽  
Vol 9 (1) ◽  
pp. 156-178
Author(s):  
Feriel Bouhadjera ◽  
Elias Ould Saïd
Keyword(s):  
Asymptotic Normality ◽  
Relative Error ◽  
Time Series Data ◽  
Asymptotic Variance ◽  
Kernel Estimator ◽  
Regression Function ◽  
Real Data ◽  
Series Data ◽  
Failure Times

Abstract Consider a survival time study, where a sequence of possibly censored failure times is observed with d-dimensional covariate The main goal of this article is to establish the asymptotic normality of the kernel estimator of the relative error regression function when the data exhibit some kind of dependency. The asymptotic variance is explicitly given. Some simulations are drawn to lend further support to our theoretical result and illustrate the good accuracy of the studied method. Furthermore, a real data example is treated to show the good quality of the prediction and that the true data are well inside in the confidence intervals.

scholarly journals ESTIMASI MODEL REGRESI SEMIPARAMETRIK MENGGUNAKAN ESTIMATOR KERNEL UNIFORM (Studi Kasus: Pasien DBD di RS Puri Raharja)

2015 ◽  
Vol 4 (4) ◽  
pp. 176
Author(s):  
ANNA FITRIANI ◽  
I GUSTI AYU MADE SRINADI ◽  
MADE SUSILAWATI
Keyword(s):  
Body Temperature ◽  
Regression Model ◽  
Linear Regression Analysis ◽  
Kernel Estimator ◽  
Semiparametric Regression ◽  
Regression Function ◽  
Multiple Linear Regression Analysis ◽  
Regression Curve ◽  
Optimal Bandwidth ◽  
Curve Estimation

Semiparametric regression model estimation is an estimation that combines both parametric and nonparametric regression model. In semiparametric regression, some of the variables are parametrics and the others are nonparametrics. Semiparametric regression is used when relationship pattern between independent and depentdent variables is half known  and half unknown. Regression curve smoothing technique in nonparametric components in this study was using uniform kernel function. The optimal semiparametric regression curve estimation was obtained by optimal bandwidth. By choosing optimal bandwidth, we would obtain a smooth regression curve estimation in respect to data pattern. In choosing optimal bandwidth, we use minimum GCV as a criteria.The purpose of this study was to estimate the semiparametric regression function of dengue fever case using uniform kernel estimator. There were 6 independent variables namely age (in years) body temperature (in Celcius), heartbeat (in times/minutes) hematocryte ratio (in percent), amount of trombocyte (× 103/ul) and fever duration ( in days). Age, body temperature, heartbeat, amount of trombosyte and fever duration are parametric components and hematocryte ration is a nonparametric component. The optimal bandwidth (h) which was obtained with minimum GCVwas 0,005. The value of MSE which was obtained by using multiple linear regression analysis was 0,031 and by using semiparametric regression was 0,00437119.

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