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.

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 Nonparametric Regression Estimation for Circular Data

Proceedings ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 27
Author(s):  
Andrea Meilán-Vila ◽  
Mario Francisco-Fernández ◽  
Rosa M. Crujeiras ◽  
Agnese Panzera
Keyword(s):  
Nonparametric Regression ◽  
Simulation Study ◽  
Regression Function ◽  
Circular Data ◽  
Regression Estimation ◽  
Response Variable ◽  
Parametric Regression ◽  
Explanatory Variables ◽  
Nonparametric Regression Estimation ◽  
Circular Regression

Non-parametric regression with a circular response variable and a unidimensional linear regressor is a topic which was discussed in the literature. In this work, we extend the results to the case of multivariate linear explanatory variables. Nonparametric procedures to estimate the circular regression function are formulated. A simulation study is carried out to study the sample performance of the proposed estimators.

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

scholarly journals Nonparametric Density and Regression Estimation

2001 ◽  
Vol 15 (4) ◽  
pp. 11-28 ◽  
Author(s):  
John DiNardo ◽  
Justin L Tobias
Keyword(s):  
Functional Form ◽  
Regression Function ◽  
Nonparametric Methods ◽  
Actual Data ◽  
Attractive Alternative ◽  
Regression Estimation ◽  
Parametric Methods ◽  
Regression Functions

We provide a nontechnical review of recent nonparametric methods for estimating density and regression functions. The methods we describe make it possible for a researcher to estimate a regression function or density without having to specify in advance a particular--and hence potentially misspecified functional form. We compare these methods to more popular parametric alternatives (such as OLS), illustrate their use in several applications, and demonstrate their flexibility with actual data and generated-data experiments. We show that these methods are intuitive and easily implemented, and in the appropriate context may provide an attractive alternative to “simpler” parametric methods.

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