Convergence rate of cross-validation in nonlinear wavelet regression estimation

1999 ◽  
Vol 44 (10) ◽  
pp. 898-901
Author(s):  
Zhang Shuanglin ◽  
Zheng Zhongguo
Keyword(s):  
Convergence Rate ◽  
Cross Validation ◽  
Regression Estimation ◽  
Wavelet Regression

Wavelet regression estimation over Lp risk based on negatively associated sample

2020 ◽  
Vol 18 (04) ◽  
pp. 2050024
Author(s):  
Huijun Guo ◽  
Junke Kou
Keyword(s):  
Convergence Rates ◽  
Regression Function ◽  
Regression Estimation ◽  
Negatively Associated ◽  
Wavelet Regression ◽  
Nonparametric Regression Estimation ◽  
Independent Case ◽  
Optimal Convergence Rates ◽  
Negatively Associated Sample ◽  
Wavelet Estimators

This paper considers wavelet estimations of a regression function based on negatively associated sample. We provide upper bound estimations over [Formula: see text] risk of linear and nonlinear wavelet estimators in Besov space, respectively. When the random sample reduces to the independent case, our convergence rates coincide with the optimal convergence rates of classical nonparametric regression estimation.

scholarly journals The One Standard Error Rule for Model Selection: Does It Work?

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 868-892
Author(s):  
Yuchen Chen ◽  
Yuhong Yang
Keyword(s):  
Variable Selection ◽  
Standard Error ◽  
Cross Validation ◽  
Housing Prices ◽  
Regression Function ◽  
Real Data ◽  
Estimation Accuracy ◽  
Regression Estimation ◽  
Large Sample Size ◽  
Estimation Formula

Previous research provided a lot of discussion on the selection of regularization parameters when it comes to the application of regularization methods for high-dimensional regression. The popular “One Standard Error Rule” (1se rule) used with cross validation (CV) is to select the most parsimonious model whose prediction error is not much worse than the minimum CV error. This paper examines the validity of the 1se rule from a theoretical angle and also studies its estimation accuracy and performances in applications of regression estimation and variable selection, particularly for Lasso in a regression framework. Our theoretical result shows that when a regression procedure produces the regression estimator converging relatively fast to the true regression function, the standard error estimation formula in the 1se rule is justified asymptotically. The numerical results show the following: 1. the 1se rule in general does not necessarily provide a good estimation for the intended standard deviation of the cross validation error. The estimation bias can be 50–100% upwards or downwards in various situations; 2. the results tend to support that 1se rule usually outperforms the regular CV in sparse variable selection and alleviates the over-selection tendency of Lasso; 3. in regression estimation or prediction, the 1se rule often performs worse. In addition, comparisons are made over two real data sets: Boston Housing Prices (large sample size n, small/moderate number of variables p) and Bardet–Biedl data (large p, small n). Data guided simulations are done to provide insight on the relative performances of the 1se rule and the regular CV.

Fully Nonparametric Regression Estimation Based on Empirical Mode Decomposition

2012 ◽  
Vol 271-272 ◽  
pp. 932-935
Author(s):  
Hong Ying Hu ◽  
Wen Long Li ◽  
Feng Qiang Zhao
Keyword(s):  
Empirical Mode Decomposition ◽  
Wavelet Decomposition ◽  
Estimation Method ◽  
Regression Function ◽  
Regression Estimation ◽  
Function Estimation ◽  
Wavelet Regression ◽  
Nonparametric Regression Estimation ◽  
Mode Decomposition ◽  
Non Stationary Signal

Empirical Mode Decomposition (EMD) is a non-stationary signal processing method developed recently. It has been applied in many engineering fields. EMD has many similarities with wavelet decomposition. But EMD Decomposition has its own characteristics, especially in accurate trend extracting. Therefore the paper firstly proposes an algorithm of extracting slow-varying trend based on EMD. Then, according to wavelet regression estimation method, a new regression function estimation method based on EMD is presented. The simulation proves the advantages of the approach with easy computation and more accurate result.

scholarly journals BIASED CROSS-VALIDATION IN A KERNEL REGRESSION ESTIMATION

1995 ◽  
Vol 8 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Jong Chul Oh ◽  
Byung Chun Kim ◽  
Jee Soo Lee ◽  
B. U. Park
Keyword(s):  
Cross Validation ◽  
Kernel Regression ◽  
Regression Estimation ◽  
Kernel Regression Estimation

scholarly journals PEMILIHAN PARAMETER PENGHALUS DALAM REGRESI SPLINE LINIER

2011 ◽  
Vol 3 (1) ◽  
pp. 9
Author(s):  
Agustini Tripena Br. Sb.
Keyword(s):  
Mean Square Error ◽  
Cross Validation ◽  
Selection Method ◽  
Regression Estimation ◽  
Mean Square ◽  
Spline Regression ◽  
Selection Methods ◽  
The Mean ◽  
Smoothing Parameters ◽  
Selection Of

This paper discusses aselection of smoothing parameters for the linier spline regression estimation on the data of electrical voltage differences in the wastewater. The selection methods are based on the mean square errorr (MSE) and generalized cross validation (GCV). The results show that in selection of smooting paranceus the mean square error (MSE) method gives smaller value , than that of the generalized cross validatio (GCV) method. It means that for our data case the errorr mean square (MSE) is the best selection method of smoothing parameter for the linear spline regression estimation.

scholarly journals PENDEKATAN REGRESI SPLINE UNTUK MEMODELKAN POLA PERTUMBUHAN BERAT BADAN BALITA

2018 ◽  
Vol 7 (3) ◽  
pp. 259
Author(s):  
NI LUH SUKERNI ◽  
I KOMANG GDE SUKARSA ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Regression Model ◽  
Cross Validation ◽  
Estimation Method ◽  
Growth Patterns ◽  
Regression Estimation ◽  
Spline Regression ◽  
Quadratic Spline ◽  
Nonparametric Regression Estimation ◽  
Weight Growth ◽  
High Flexibility

The study is aimed to estimate the best spline regression model for toddler’s weight growth patterns. Spline is one of the nonparametric regression estimation method which has a high flexibility and is able to handle data that change in particular subintervals so thus resulting in model which fitted the data. This study uses data of toddler’s weight growth at Posyandu Mekar Sari, Desa Suwug, Kabupaten Buleleng. The best spline regression model is chosen based on the minimum Generalized Cross Validation (GCV) value. The study shows that the best spline regression model for the data is quadratic spline regression model with six optimal knot points. The minimum GCV value is 0,900683471925 with the determination coefficient  equals to 0,954609.

scholarly journals ANALISIS REGRESI NONPARAMETRIK SPLINE MULTIVARIAT UNTUK PEMODELAN INDIKATOR KEMISKINAN DI INDONESIA

2016 ◽  
Vol 5 (3) ◽  
pp. 111 ◽  
Author(s):  
DESAK AYU WIRI ASTITI ◽  
I WAYAN SUMARJAYA ◽  
MADE SUSILAWATI
Keyword(s):  
Nonparametric Regression ◽  
Cross Validation ◽  
Social Economy ◽  
Estimation Method ◽  
Regression Method ◽  
Regression Estimation ◽  
Multivariate Spline ◽  
Nonparametric Regression Estimation ◽  
Poverty Indicators ◽  
The Relationship

The aim of this study is to obtain statistics models which explain the relationship between variables that influence the poverty indicators in Indonesia using multivariate spline nonparametric regression method. Spline is a nonparametric regression estimation method that is automatically search for its estimation wherever the data pattern move and thus resulting in model which fitted the data. This study, uses data from survey of Social Economy National (Susenas) and survey of Employment National (Sakernas) of 2013 from the publication of the Central Bureau of Statistics (BPS). This study yields two models which are the best model from two used response variables. The criterion uses to select the best model is the minimum Generalized Cross Validation (GCV). The best spline model obtained is cubic spline model with five optimal knots.

scholarly journals Wavelet regression estimation in nonparametric mixed effect models

2003 ◽  
Vol 85 (2) ◽  
pp. 267-291 ◽  
Author(s):  
Claudia Angelini ◽  
Daniela De Canditiis ◽  
Frédérique Leblanc
Keyword(s):  
Regression Estimation ◽  
Mixed Effect ◽  
Wavelet Regression ◽  
Mixed Effect Models
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