TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL

Title & Authors
TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
Huang, Zhensheng; Zhang, Riquan;

Abstract
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\small{\chi^2}$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
Keywords
averaged method;back-fitting algorithms;generalized likelihood ratio test;local linear method;varying-coefficient single-index model;Wilks phenomenon;
Language
English
Cited by
1.
Empirical likelihood-based inference in varying-coefficient single-index models,;

Journal of the Korean Statistical Society, 2011. vol.40. 2, pp.205-215
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Inference for Nonparametric Parts in Single-Index Varying-Coefficient Model, Communications in Statistics - Theory and Methods, 2012, 41, 7, 1214
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Empirical likelihood-based inference in varying-coefficient single-index models, Journal of the Korean Statistical Society, 2011, 40, 2, 205
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Generalized Analysis-of-variance-type Test for the Single-index Quantile Model, Communications in Statistics - Theory and Methods, 2015, 44, 13, 2842
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Empirical likelihood for varying-coefficient single-index model with right-censored data, Metrika, 2012, 75, 1, 55
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Efficient penalized estimating method in the partially varying-coefficient single-index model, Journal of Multivariate Analysis, 2013, 114, 189
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