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Simultaneous Inference for the Partially Linear Model with a Multivariate Unknown Function when the Covariates are Measured with Errors

Author

Listed:
  • Kun Ho Kim
  • Wolfgang K. Härdle
  • Shih-Kang Chao

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 confidence 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.

Suggested Citation

  • Kun Ho Kim & Wolfgang K. Härdle & Shih-Kang Chao, 2016. "Simultaneous Inference for the Partially Linear Model with a Multivariate Unknown Function when the Covariates are Measured with Errors," SFB 649 Discussion Papers SFB649DP2016-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2016-024
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Measurement error; Partially linear model; Regression calibration; Non-parametric function; Semi-parametric regression; Uniform confidence 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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