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Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation

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Abstract

This paper presents several stochastic equicontinuity results that are useful for establishing the asymptotic properties of estimators and tests in parametric, semiparametric, and nonparametric econometric models. In particular, they can be applied straightforwardly in the estimation and testing results of Andrews (1989b). The paper takes various stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive conditions under which the entropy conditions hold. This yields stochastic equicontinuity results that are readily applicable in a variety of contexts. This paper also presents a number of consistency results for nonparametric kernel estimators of density and regression functions and their derivatives. These results are particularly useful in semiparametric estimation and testing problems that rely on preliminary nonparametric estimators, as in Andrews (1989b). The results allow for near epoch dependent non-identically distributed random variables, data-dependent bandwidth sequences, preliminary estimation of parameters (e.g., regression based on residuals), and nonparametric regression on index functions. Some of the results make use of the stochastic equicontinuity results of the paper.

Suggested Citation

  • Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation," Cowles Foundation Discussion Papers 909R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1990.
    • Handle: RePEc:cwl:cwldpp:909r
    Note: CFP 863.
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    Cited by:

    1. Tae-Hwan Kim & Christophe Muller, 2020. "Inconsistency transmission and variance reduction in two-stage quantile regression," Post-Print hal-02084505, HAL.
    2. Corradi, Valentina & Distaso, Walter & Swanson, Norman R., 2009. "Predictive density estimators for daily volatility based on the use of realized measures," Journal of Econometrics, Elsevier, vol. 150(2), pages 119-138, June.
    3. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    4. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318.
    5. Tae-Hwan Kim, & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," AMSE Working Papers 1221, Aix-Marseille School of Economics, France.
    6. Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation for Research in Economics, Yale University.

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