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Nonparametric Knn estimation with monotone constraints


  • Zheng Li
  • Guannan Liu
  • Qi Li


The K-nearest-neighbor (Knn) method is known to be more suitable in fitting nonparametrically specified curves than the kernel method (with a globally fixed smoothing parameter) when data sets are highly unevenly distributed. In this paper, we propose to estimate a nonparametric regression function subject to a monotonicity restriction using the Knn method. We also propose using a new convergence criterion to measure the closeness between an unconstrained and the (monotone) constrained Knn-estimated curves. This method is an alternative to the monotone kernel methods proposed by Hall and Huang (2001), and Du et al. (2013). We use a bootstrap procedure for testing the validity of the monotone restriction. We apply our method to the “Job Market Matching” data taken from Gan and Li (2016) and find that the unconstrained/constrained Knn estimators work better than kernel estimators for this type of highly unevenly distributed data.

Suggested Citation

  • Zheng Li & Guannan Liu & Qi Li, 2017. "Nonparametric Knn estimation with monotone constraints," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 988-1006, October.
  • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:988-1006
    DOI: 10.1080/07474938.2017.1307904

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    References listed on IDEAS

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    Cited by:

    1. Tai-Hsin Huang & Yi-Huang Chiu & Chih-Ying Mao, 2021. "Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 273-303, June.
    2. Wang, Shaoping & Li, Ang & Wen, Kuangyu & Wu, Ximing, 2020. "Robust kernels for kernel density estimation," Economics Letters, Elsevier, vol. 191(C).
    3. Eunji Lim & Kihwan Kim, 2020. "Estimating Smooth and Convex Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(5), pages 1-40, September.
    4. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.

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