Identification of Non-Varying Coefficients in Varying-Coefficient Models

Identification of Non-Varying Coefficients in Varying-Coefficient Models A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F-approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Identification of Non-Varying Coefficients in Varying-Coefficient Models

Identification of Non-Varying Coefficients in Varying-Coefficient Models

Acta Mathematicae Applicatae Sinica, English Series Vol. 21, No. 1 (2005) 135–144 Identification of Non-Varying Coefficients in Varying-Coefficient Models Chang-lin Mei, Chun-xia Zhang School of Science, Xi’an Jiaotong University, Xi’an 710049, China (E-Mail: clmei@mail.xjtu.edu.cn) Abstract A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know apriori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F -approximation and three-moment χ approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory. Keywords varying-coefficient model; partially varying-coefficient model; local linear fitting; three-moment χ approximation; F -approximation 2000 MR Subject Classification 62J02; 62G05 1 Introduction It has been well known that a varying-coefficient model is a useful extension of a linear model by allowing all the coefficients to vary as unknown functions of another factor. Specifically, let Y be the response variable and X ,X ,··· ,X as well as U be the explanatory variables. Then, 1 2 p based on n observations (y ; u ; x ,x ,··· ,x )(i =1, 2,··· ,n), the varying-coefficient model i i i1 i2 ip has...
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Publisher
Springer-Verlag
Copyright
Copyright © 2005 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-005-0224-0
Publisher site
See Article on Publisher Site

Abstract

A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F-approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2005

References

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