scholarly journals Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jia Chen ◽  
Junke Kou
Keyword(s):  
Multiplicative Noise ◽  
Convergence Rates ◽  
Linear Estimator ◽  
Estimation Model ◽  
Functional Estimation ◽  
Nonparametric Regression Estimation ◽  
Pointwise Error ◽  
Regression Estimators ◽  
Pointwise Estimation ◽  
Nonparametric Functional Estimation

In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation.

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 Two-scale method for the Monge–Ampère equation: pointwise error estimates

2018 ◽  
Vol 39 (3) ◽  
pp. 1085-1109 ◽  
Author(s):  
R H Nochetto ◽  
D Ntogkas ◽  
W Zhang
Keyword(s):  
Error Estimates ◽  
Viscosity Solution ◽  
Continuous Dependence ◽  
Convergence Rates ◽  
Classical Solutions ◽  
Discrete Version ◽  
Scale Method ◽  
Pointwise Error ◽  
Pointwise Error Estimates ◽  
Monge Ampere

Abstract In this paper we continue the analysis of the two-scale method for the Monge–Ampère equation for dimension d ≥ 2 introduced in the study by Nochetto et al. (2017, Two-scale method for the Monge–Ampère equation: convergence to the viscosity solution. Math. Comput., in press). We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete version of the Alexandroff estimate. They are both instrumental to prove pointwise error estimates for classical solutions with Hölder and Sobolev regularity. We also derive convergence rates for viscosity solutions with bounded Hessians which may be piecewise smooth or degenerate.

scholarly journals LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES

2012 ◽  
Vol 28 (5) ◽  
pp. 935-958 ◽  
Author(s):  
Degui Li ◽  
Zudi Lu ◽  
Oliver Linton
Keyword(s):  
Convergence Rates ◽  
Regression Function ◽  
Linear Estimator ◽  
Uniform Consistency ◽  
Linear Fitting ◽  
Semiparametric Modeling ◽  
Local Linear Fitting ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Nonparametric Kernel

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

scholarly journals Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise

2021 ◽  
Author(s):  
Ladislas Jacobe de Naurois ◽  
Arnulf Jentzen ◽  
Timo Welti
Keyword(s):  
Wave Equation ◽  
Weak Convergence ◽  
Wave Equations ◽  
Multiplicative Noise ◽  
Convergence Rates ◽  
Rates Of Convergence ◽  
Kolmogorov Equation ◽  
Continuous Version ◽  
Stochastic Wave Equations ◽  
Galerkin Approximations

AbstractStochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved explicitly, but the literature contains a number of results which show that numerical approximation processes converge with suitable rates of convergence to solutions of such equations. In the case of approximation results for strong convergence rates, semilinear stochastic wave equations with both additive or multiplicative noise have been considered in the literature. In contrast, the existing approximation results for weak convergence rates assume that the diffusion coefficient of the considered semilinear stochastic wave equation is constant, that is, it is assumed that the considered wave equation is driven by additive noise, and no approximation results for multiplicative noise are known. The purpose of this work is to close this gap and to establish essentially sharp weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. In particular, our weak convergence result establishes as a special case essentially sharp weak convergence rates for the continuous version of the hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov equation and the Hölder-inequality for Schatten norms.

scholarly journals Supervised Linear Estimator Modeling (SLEMH) for Health Monitoring

2019 ◽  
Vol 9 (1) ◽  
pp. 2876-2882
Keyword(s):  
Health Monitoring ◽  
Research Work ◽  
Health Indicators ◽  
Health Condition ◽  
Recursive Feature Elimination ◽  
Linear Estimator ◽  
Health States ◽  
Linear Discriminant ◽  
Health Monitoring System ◽  
Regression Estimators

In this research work, the E-Health monitoring system has been developed using fifteen health indicators. These fifteen features were selected by following a Recursive Feature Elimination with Cross-Validation method. The dataset was labeled as per medical limits and segregated into three classes (normal, borderline and onset of unhealthy state). A rigorous process was followed at each step to find out which linear estimator and model is suitable for classifying health condition of persons. Five regression estimators were evaluated and it was found that logistic regression and linear discriminant analysis methods are providing highest accuracy and lowest error for classifying three health states of a patient.

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