Premium
Generalized likelihood ratio tests for the structure of semiparametric additive models
Author(s) -
Jiang Jiancheng,
Zhou Haibo,
Jiang Xuejun,
Peng Jianan
Publication year - 2007
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550350304
Subject(s) - nonparametric statistics , semiparametric regression , multivariate statistics , mathematics , smoothing , semiparametric model
Semiparametric additive models (SAMs) are very useful in multivariate nonparametric regression. In this paper, the authors study nonparametric testing problems for the nonparametric components of SAMs. Using the backfitting algorithm and the local polynomial smoothing technique, they extend to SAMs the generalized likelihood ratio tests of Fan &Jiang (2005). The authors show that the proposed tests possess the Wilks‐type property and that they can detect alternatives nearing the null hypothesis with a rate arbitrarily close to root‐ n while error distributions are unspecified. They report simulations which demonstrate the Wilks phenomenon and the powers of their tests. They illustrate the performance of their approach by simulation and using the Boston housing data set.