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Uniform Convergence of Weighted Sums of Non- and Semi-parametric Residuals for Estimation and Testing

Author

Listed:
  • Juan Carlos Escanciano

    (Indiana University)

  • David Jacho-Chavez

    (Indiana University)

  • Arthur Lewbel

    (Boston College)

Abstract

A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidth, random trimming, and estimated weights. An extension allows for generated regressors, without requiring the calculation of functional derivatives. Example applications are provided for a binary choice model with selection, including a new semiparametric maximum likelihood estimator, and a new directional test for correct specification of the average structural function. An extended Appendix contains general results on uniform rates for kernel estimators, additional applications, and primitive sufficient conditions for high level assumptions.

Suggested Citation

  • Juan Carlos Escanciano & David Jacho-Chavez & Arthur Lewbel, 2010. "Uniform Convergence of Weighted Sums of Non- and Semi-parametric Residuals for Estimation and Testing," Boston College Working Papers in Economics 756, Boston College Department of Economics, revised 31 Jan 2012.
    • Handle: RePEc:boc:bocoec:756
    Note: Previously circulated as "Uniform Convergence for Semiparametric Two Step Estimators and Tests"
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    More about this item

    Keywords

    Double index models; Two step estimators; Semiparametric regression; Control function estimators; Sample selection models; Empirical process theory; Limited dependent variables; Oracle estimators; Migration;
    All these keywords.

    JEL classification:

    • 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
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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