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

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  • Hai Wang
  • Xinjie Chen
  • Nancy Flournoy

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Hai Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:99-113
    DOI: 10.1007/s00362-014-0645-z
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    References listed on IDEAS

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    1. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    3. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    4. Hjort, Nils Lid & Claeskens, Gerda, 2006. "Focused Information Criteria and Model Averaging for the Cox Hazard Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1449-1464, December.
    5. Gerda Claeskens & Raymond J. Carroll, 2007. "An asymptotic theory for model selection inference in general semiparametric problems," Biometrika, Biometrika Trust, vol. 94(2), pages 249-265.
    6. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    7. Schomaker, Michael & Wan, Alan T.K. & Heumann, Christian, 2010. "Frequentist Model Averaging with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3336-3347, December.
    8. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
    9. Xinyu Zhang & Alan Wan & Sherry Zhou, 2012. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142.
    10. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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    2. Lee, JooChul & Wang, HaiYing & Schifano, Elizabeth D., 2020. "Online updating method to correct for measurement error in big data streams," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).

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