We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated-i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have optimality properties and computational advantages that are similar to those of the classical score tests in the parametric model framework. The test procedures are applicable to several semiparametric extensions of measurement error models, including when the measurement error distribution is estimated non-parametrically as well as for generalized partially linear models. The performance of the local score-type and omnibus goodness-of-fit tests is demonstrated through simulation studies and analysis of a nutrition data set.
|Original language||English (US)|
|Number of pages||18|
|Journal||Journal of the Royal Statistical Society: Series B (Statistical Methodology)|
|State||Published - Sep 14 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Carroll and Ma's research was supported by a grant from the National Cancer Institute (CA57030). Carroll and Hart's work was also supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology. Ma's work is supported by National Science Foundation grant DMS-0906341, and Hart's was partially supported by National Science Foundation grant DMS-0604801. Janicki's work was done while at the University of Maryland. He thanks his adviser Professor Abram Kagan for his advice and support.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.