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

, Volume 21 (1) – Jan 1, 2005

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 Journals
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

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