scholarly journals Estimation of the Derivatives of a Function in a Convolution Regression Model with Random Design

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Christophe Chesneau ◽  
Maher Kachour
Keyword(s):  
Regression Model ◽  
Unknown Function ◽  
Convolution Product ◽  
Random Design ◽  
Function Element ◽  
Wavelet Methods ◽  
Derivatives Of

A convolution regression model with random design is considered. We investigate the estimation of the derivatives of an unknown function, element of the convolution product. We introduce new estimators based on wavelet methods and provide theoretical guarantees on their good performances.

Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

2002 ◽  
Vol 9 (3) ◽  
pp. 431-448
Author(s):  
A. Bychowska
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Unknown Function ◽  
Functional Dependence ◽  
Nonlinear Parabolic Equations ◽  
Quasilinearization Method ◽  
Convergence Theorems ◽  
Nonlinear Parabolic ◽  
Quasilinearization Methods ◽  
Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

An Isoparametric Finite Element With Nodal Derivatives

1981 ◽  
Vol 48 (1) ◽  
pp. 64-68
Author(s):  
W. D. Webster
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Unknown Function ◽  
Nodal Point ◽  
Shape Functions ◽  
Isoparametric Element ◽  
Partial Derivatives ◽  
Isoparametric Finite Element ◽  
Local Coordinates ◽  
Derivatives Of

A finite element using the nodal point values of the first partial derivatives of the unknown function with respect to the coordinates to increase the order of the resulting interpolating polynomial is formulated as an isoparametric element. The shape functions in local coordinates are given and then to satisfy requirements for the transformation of derivatives are modified for use with the global coordinates. Examples of a cantilever beam, a curved cantilever beam, and a flat bar with a hole demonstrate the high-order capabilities of the element. The advantages of the element over other isoparametric elements are discussed.

scholarly journals The Estimation of Residual Variance in Nonparametric Regression

2021 ◽  
Vol 17 (3) ◽  
pp. 438-446
Author(s):  
Abdul Wahab ◽  
I Nyoman Budiantara ◽  
Kartika Fitriasari
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Unknown Function ◽  
Residual Variance ◽  
Variance Estimator ◽  
Nonparametric Regression Model ◽  
Data Simulation ◽  
Independent Variable ◽  
Variable G

Given a nonparametric regression model Yi = g(xi) + ei,    i = 1, 2, …, n, where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows: . The biased value of residual variance estimator of the Rice method is: , where  and. Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is: , Where   , , , , ,  k = 1, 2, … , m. Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.

scholarly journals Strong consistency of regression function estimator with martingale difference errors

2021 ◽  
Vol 19 (1) ◽  
pp. 1056-1068
Author(s):  
Yingxia Chen
Keyword(s):  
Strong Convergence ◽  
Regression Model ◽  
Unknown Function ◽  
Strong Consistency ◽  
Regression Function ◽  
Martingale Difference ◽  
Nonparametric Estimator ◽  
Convergence Properties ◽  
Fixed Design

Abstract In this paper, we consider the regression model with fixed design: Y i = g ( x i ) + ε i {Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i} , 1 ≤ i ≤ n 1\le i\le n , where { x i } \left\{{x}_{i}\right\} are the nonrandom design points, and { ε i } \left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and g g is an unknown function. Nonparametric estimator g n ( x ) {g}_{n}\left(x) of g ( x ) g\left(x) will be introduced and its strong convergence properties are established.

scholarly journals On a Langevin equation involving Caputo fractional proportional derivatives with respect to another function

2021 ◽  
Vol 7 (1) ◽  
pp. 1273-1292
Author(s):  
Zaid Laadjal ◽  
◽  
Fahd Jarad ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Gamma Function ◽  
Langevin Equation ◽  
Unknown Function ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
The Given ◽  
Derivatives Of ◽  
Theoretical Results

<abstract><p>In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.</p></abstract>

scholarly journals Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

2017 ◽  
Vol 15 (1) ◽  
pp. 768-786
Author(s):  
Yuliya Gorban
Keyword(s):  
Dirichlet Problem ◽  
Present Article ◽  
Unknown Function ◽  
Entropy Solutions ◽  
Independent Variables ◽  
Nonlinear Elliptic ◽  
Weighted Functions ◽  
Rates Of Growth ◽  
Derivatives Of ◽  
Second Order Equations

Abstract In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of ℝn(n ⩾ 2) . This class is described by the presence of a set of exponents q1,…, qn and a set of weighted functions ν1,…, νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to investigate the existence of entropy solutions of the problem under consideration.

scholarly journals A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Christophe Chesneau
Keyword(s):  
Regression Function ◽  
Rates Of Convergence ◽  
Nonparametric Regression Model ◽  
Random Design ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean ◽  
Derivatives Of ◽  
Wavelet Estimators ◽  
Fast Rates

We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions.

scholarly journals The Gasser-Müller estimator

2004 ◽  
Vol 52 (3) ◽  
pp. 167-176 ◽  
Author(s):  
Jitka Poměnková
Keyword(s):  
Regression Model ◽  
Kernel Smoothing ◽  
Data Sets ◽  
Data Set ◽  
Random Design ◽  
Fixed Design ◽  
Fixed Design Regression

Kernel smoothing provides a simple way for finding structure in data. The idea of the kernel smoothing can be applied to a simple fixed design regression model and a random design regression model. This article is focused on kernel smoothing for fixed design regression model with using special type of estimator, the Gasser-Müller estimator, and on choice of the bandwidth. At the end of this article figures for ilustration described methods on two data sets are shown. The first data set contains simulated values of function sin(2πx), the second contains January average temperatures measured in Basel 1755–1855.

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