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Nonparametric Sample Splitting

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Abstract

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. Our model has broad empirical relevance as illustrated by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery. We find that the new empirical results are substantially different from the existing studies.

Suggested Citation

  • Yoonseok Lee & Yulong Wang, 2020. "Nonparametric Sample Splitting," Center for Policy Research Working Papers 222, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:222
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    File URL: https://surface.syr.edu/cpr/254/
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    Cited by:

    1. Yoonseok Lee & Yulong Wang, 2020. "Inference in Threshold Models," Center for Policy Research Working Papers 223, Center for Policy Research, Maxwell School, Syracuse University.

    More about this item

    Keywords

    Sample Splitting; Threshold; Nonparametric; Random Field; Tipping Point; Metropolitan Area Boundary;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics

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