The focused information criterion for varying-coefficient partially linear measurement error models

• Published in: Statistical papers (Berlin, Germany) Vol. 57; no. 1; pp. 99 - 113
• Main Authors: Wang, Hai Ying, Chen, Xinjie, Flournoy, Nancy
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016; Springer Nature B.V
• Subjects: Asymptotic properties; Criteria; Diet; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Error analysis; Estimators; Finance; Food intake; Insurance; Management; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Measurement errors; Nutrition; Operations Research/Decision Theory; Parameter estimation; Permissible error; Probability Theory and Stochastic Processes; Random variables; Regular Article; Samples; Statistical analysis; Statistics; Statistics for Business; Studies; United States > US; Focused information criterion; Measurement errors; Model selection; Semi-parametric models; Model averaging
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-014-0645-z

Under general parametric models, Claeskens and Hjort (J Am Stat Assoc 98:900–916, 2003 ) proposed a focused information criterion for model selection which emphasizes the accuracy of estimation for particular parameters of interest. This paper extends their framework to include a semi-parametric varying-coefficient partially linear model when covariates in both the parametric and the non-parametric parts are subject to measurement errors. We allow the covariance matrices of the measurement errors to be unknown and be estimated by replicated observations. Also, we derive the asymptotic properties of the frequentist model average estimator for the model in consideration, which generalizes the results obtained by Wang et al. (Electron J Stat 6:1017–1039, 2012 ). In addition to asymptotic properties, finite sample performance of the proposed methods are examined in a simulation study, and a data set obtained from Continuing Survey of Food Intakes by Individuals conducted by the U.S. Department of Agriculture’s (CSFII) is considered.