scholarly journals Variable bandwidth kernel regression estimation

2021 ◽  
Author(s):  
Janet Nakarmi ◽  
Hailin Sang ◽  
Lin Ge
Keyword(s):  
Limit Theorems ◽  
Kernel Method ◽  
Kernel Regression ◽  
Regression Function ◽  
Order Derivative ◽  
Variable Kernel ◽  
Variable Bandwidth ◽  
Regression Estimators ◽  
Kernel Regression Estimation ◽  
Fifth Order

In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

Kernel Regression Estimation for Functional Data

2018 ◽  
Author(s):  
Frédéric Ferraty ◽  
Philippe Vieu
Keyword(s):  
Kernel Methods ◽  
Functional Data ◽  
Linear Functional ◽  
Kernel Smoothing ◽  
Kernel Regression ◽  
Functional Regression ◽  
Regression Estimation ◽  
Asymptotic Results ◽  
Kernel Regression Estimation ◽  
The Impact

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.

scholarly journals Random Noise Suppression of Magnetic Resonance Sounding Data with Intensive Sampling Sparse Reconstruction and Kernel Regression Estimation

2019 ◽  
Vol 11 (15) ◽  
pp. 1829 ◽  
Author(s):  
Yao ◽  
Zhang ◽  
Yu ◽  
Zhao ◽  
Sun
Keyword(s):  
Magnetic Resonance ◽  
Field Experiments ◽  
Noise Suppression ◽  
Random Noise ◽  
Kernel Regression ◽  
Sparse Reconstruction ◽  
Regression Estimation ◽  
Magnetic Resonance Sounding ◽  
Kernel Regression Estimation ◽  
Intensive Sampling

The magnetic resonance sounding (MRS) method is a non-invasive, efficient and advanced geophysical method for groundwater detection. However, the MRS signal received by the coil sensor is extremely susceptible to electromagnetic noise interference. In MRS data processing, random noise suppression of noisy MRS data is an important research aspect. We propose an approach for intensive sampling sparse reconstruction (ISSR) and kernel regression estimation (KRE) to suppress random noise. The approach is based on variable frequency sampling, numerical integration and statistical signal processing combined with kernel regression estimation. In order to realize the approach, we proposed three specific sparse reconstructions, namely rectangular sparse reconstruction, trapezoidal sparse reconstruction and Simpson sparse reconstruction. To solve the distortion of peaks and valleys after sparse reconstruction, we introduced the KRE to deal with the processed data by the ISSR. Further, the simulation and field experiments demonstrate that the ISSR-KRE approach is a feasible and effective way to suppress random noise. Besides, we find that rectangular sparse reconstruction and trapezoidal sparse reconstruction are superior to Simpson sparse reconstruction in terms of noise suppression effect, and sampling frequency is positively correlated with signal-to-noise improvement ratio (SNIR). In one case of field experiment, the standard deviation of noisy MRS data was reduced from 1200.80 nV to 570.01 nV by the ISSR-KRE approach. The proposed approach provides theoretical support for random noise suppression and contributes to the development of MRS instrument with low power consumption and high efficiency. In the future, we will integrate the approach into MRS instrument and attempt to utilize them to eliminate harmonic noise from power line.

scholarly journals Local adaptive smoothing in kernel regression estimation

2010 ◽  
Vol 80 (7-8) ◽  
pp. 540-547 ◽  
Author(s):  
Qi Zheng ◽  
K.B. Kulasekera ◽  
Colin Gallagher
Keyword(s):  
Kernel Regression ◽  
Regression Estimation ◽  
Adaptive Smoothing ◽  
Kernel Regression Estimation

Chebyshev-Legendre Pseudo-Spectral Method for the Modified Kawahara Equation

2010 ◽  
Vol 143-144 ◽  
pp. 191-195 ◽  
Author(s):  
Ting Gang Zhao ◽  
Yan Tang Liang ◽  
He Ping Ma
Keyword(s):  
Computational Complexity ◽  
Spectral Method ◽  
Order Derivative ◽  
Kawahara Equation ◽  
Numerical Tests ◽  
Derivative Term ◽  
Galerkin Formulation ◽  
Pseudo Spectral Method ◽  
Fifth Order ◽  
Pseudo Spectral

Chebyshev-Legendre pseudo-spectral method was applied to resolve the modified Kawahara equation. The proposed approach is based on Legendre-Petrov Galerkin formulation but only the Chebyshev-Gauss-Lobatto nodes are used in the computation. The Petrov method is considered for the unsymmetry of the fifth-order derivative term appeared in the modified Kawahara equation and Chebyshev-Legendre method is used for reducing the computational complexity. Numerical tests are presented to verify the efficiency of the proposed approach.

High-quantile regression for tail-dependent time series

Biometrika ◽  
2020 ◽  
Author(s):  
Ting Zhang
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Limit Theorems ◽  
Tail Dependence ◽  
Serial Dependence ◽  
Response Distribution ◽  
Tail Region ◽  
Strongly Mixing ◽  
Regression Estimators ◽  
High Quantile

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.

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