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Simultaneous inference for the partially linear model with a multivariate unknown function when the covariates are measured with errors

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  • Kim, Kun Ho
  • Chao, Shih-Kang
  • Härdle, Wolfgang Karl

Abstract

In this paper, we analyze the nonparametric part of a partially linear model when the covariates in parametric and non-parametric parts are subject to measurement errors. Based on a two-stage semi-parametric estimate, we construct a uniform con dence surface of the multivariate function for simultaneous inference. The developed methodology is applied to perform inference for the U.S. gasoline demand where the income and price variables are measured with errors. The empirical results strongly suggest that the linearity of the U.S. gasoline demand is rejected.

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  • Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2016. "Simultaneous inference for the partially linear model with a multivariate unknown function when the covariates are measured with errors," SFB 649 Discussion Papers 2016-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-024
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    References listed on IDEAS

    as
    1. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2012. "Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation," Quantitative Economics, Econometric Society, vol. 3(1), pages 29-51, March.
    2. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
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    More about this item

    Keywords

    Measurement error; Partially linear model; Regression calibration; Non-parametric function; Semi-parametric regression; Uniform con dence surface; Simultaneous inference; U.S. Gasoline demand; Non-linearity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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