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Consistent model specification tests based on k-nearest-neighbor estimation method

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  • Li, Hongjun
  • Li, Qi
  • Liu, Ruixuan

Abstract

We propose a simple consistent test for a parametric regression functional form based on k-nearest-neighbor (k-nn) method. We derive the null distribution of the test statistic and show that the test achieves the minimax rate optimality against smooth alternatives. A wild bootstrap method is used to better approximate the null distribution of the test statistic. We also propose a k-nn statistic which tests for omitted variables nonparametrically. Simulations and an empirical application using US economics new Ph.D. job market matching data show that the k-nn method is more appropriate than the kernel method to analyze unevenly distributed data.

Suggested Citation

  • Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:1:p:187-202
    DOI: 10.1016/j.jeconom.2016.03.004
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    Cited by:

    1. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2023. "Optimal minimax rates of specification testing with data-driven bandwidth," Econometric Reviews, Taylor & Francis Journals, vol. 42(6), pages 487-512, June.
    2. Wang, Wenju & Wang, Qiao, 2019. "Consistent specification test for partially linear models with the k-nearest-neighbor method," Economics Letters, Elsevier, vol. 177(C), pages 89-93.
    3. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    4. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.

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    Keywords

    k-nearest-neighbor method; Consistent test; Bootstrap; Empirical application;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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