Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors

2020 ◽  
Vol 33 (4) ◽  
pp. 1212-1243
Author(s):  
Liwang Ding ◽  
Ping Chen ◽  
Qiang Zhang ◽  
Yongming Li
Keyword(s):  
Asymptotic Normality ◽  
Semiparametric Model ◽  
Random Errors ◽  
Wavelet Estimators

A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors

2019 ◽  
Vol 69 (6) ◽  
pp. 1471-1484
Author(s):  
Liwang Ding ◽  
Ping Chen
Keyword(s):  
Numerical Simulation ◽  
Regression Model ◽  
Nonparametric Regression ◽  
Random Variables ◽  
Random Errors ◽  
Nonparametric Regression Model ◽  
Moment Conditions ◽  
Widely Orthant Dependent ◽  
The Moment ◽  
Wavelet Estimators

Abstract In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.

scholarly journals Asymptotic properties of wavelet estimators in heteroscedastic semiparametric model based on negatively associated innovations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xueping Hu ◽  
Jinbiao Zhong ◽  
Jiashun Ren ◽  
Bing Shi ◽  
Keming Yu
Keyword(s):  
Strong Consistency ◽  
Closed Interval ◽  
Asymptotic Properties ◽  
Semiparametric Regression ◽  
Slope Parameter ◽  
Random Errors ◽  
Semiparametric Regression Model ◽  
Negatively Associated ◽  
Na Random Variables ◽  
Wavelet Estimators

AbstractConsider the heteroscedastic semiparametric regression model $y_{i}=x_{i}\beta+g(t_{i})+\varepsilon_{i}$yi=xiβ+g(ti)+εi, $i=1, 2, \ldots, n$i=1,2,…,n, where β is an unknown slope parameter, $\varepsilon_{i}=\sigma_{i}e_{i}$εi=σiei, $\sigma^{2}_{i}=f(u_{i})$σi2=f(ui), $(x_{i},t_{i},u_{i})$(xi,ti,ui) are nonrandom design points, $y_{i}$yi are the response variables, f and g are unknown functions defined on the closed interval $[0,1]$[0,1], random errors $\{e_{i} \}${ei} are negatively associated (NA) random variables with zero means. Whereas kernel estimators of β, g, and f have attracted a lot of attention in the literature, in this paper, we investigate their wavelet estimators and derive the strong consistency of these estimators under NA error assumption. At the same time, we also obtain the Berry–Esséen type bounds of the wavelet estimators of β and g.

scholarly journals Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models

Metrika ◽  
2021 ◽  
Author(s):  
Fritjof Freise ◽  
Norbert Gaffke ◽  
Rainer Schwabe
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Parameter Space ◽  
Generalized Linear Models ◽  
Nonlinear Regression ◽  
Linear Models ◽  
Nonlinear Models ◽  
Random Errors ◽  
True Parameter ◽  
Least Squares Estimators

AbstractThe paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

Statistics and parallaxes

1978 ◽  
Vol 48 ◽  
pp. 7-29
Author(s):  
T. E. Lutz
Keyword(s):  
Experimental Design ◽  
Statistical Methods ◽  
Review Paper ◽  
Systematic Errors ◽  
Past Experience ◽  
Random Errors ◽  
Trigonometric Parallaxes ◽  
Systematic And Random Errors

This review paper deals with the use of statistical methods to evaluate systematic and random errors associated with trigonometric parallaxes. First, systematic errors which arise when using trigonometric parallaxes to calibrate luminosity systems are discussed. Next, determination of the external errors of parallax measurement are reviewed. Observatory corrections are discussed. Schilt’s point, that as the causes of these systematic differences between observatories are not known the computed corrections can not be applied appropriately, is emphasized. However, modern parallax work is sufficiently accurate that it is necessary to determine observatory corrections if full use is to be made of the potential precision of the data. To this end, it is suggested that a prior experimental design is required. Past experience has shown that accidental overlap of observing programs will not suffice to determine observatory corrections which are meaningful.

Asymptotic normality of processes with a branching structure

1998 ◽  
Vol 14 (4) ◽  
pp. 833-848
Author(s):  
Malcolm P. Quine ◽  
Władysław Szczotka
Keyword(s):  
Asymptotic Normality

STUDY OF INACCURACY IN THE OPERATION OF THE MAIN CONTROLLER OF STB MACHINE

2019 ◽  
Keyword(s):  
Normal Distribution ◽  
Stable Process ◽  
Random Errors ◽  
Actual Length ◽  
Experimental Data Processing ◽  
Set Up ◽  
Main Regulator ◽  
Transmission Gear ◽  
Selection Of

At production of fabrics, including fabrics for agricultural purpose, an important role is played by the cor-rect adjustment of operation of machine main regulator. The quality of setup of machine main controller is determined by the proper selection of rotation angle of warp beam weaving per one filling thread. In the pro-cess of using the regulator as a result of mistakes in adjustment, wear of transmission gear and backlashes in connections of details there are random changes in threads length. The purpose of the article is the research of property of random errors of basis giving by STB machine regulator. Mistakes can be both negative, and positive. In case of emergence only negative or only positive mistakes operation of the machine becomes im-possible as there will be a consecutive accumulation of mistakes. As a result of experimental data processing for stable process of weaving and the invariable diameter of basis threads winding of threads it is revealed that the random error of giving is set up as linear function of the accidental length having normal distribution. Measurements of accidental deviations in giving of a basis by the main regulator allowed to construct a curve of normal distribution of its actual length for one pass of weft thread. The presented curve of distribution of random errors in giving of a basis is the displaced curve of normal distribution of the accidental sizes. Also we define the density of probability of normal distribution of basis giving errors connected with a margin er-ror operation of the main regulator knowing of which allows to plan ways of their decrease that is important for improvement of quality of the produced fabrics.

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