Local and omnibus goodness-of-fit tests in classical measurement error models

Yanyuan Ma, Jeffrey D. Hart, Ryan Janicki, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)81-98
Number of pages18
JournalJournal of the Royal Statistical Society: Series B (Statistical Methodology)
Volume73
Issue number1
DOIs
StatePublished - Sep 14 2010
Externally publishedYes

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