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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0909-r.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 909R.

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Length: 98 pages
Date of creation: 1989
Date of revision: Jul 1990
Publication status: Published in Econometrica, 62(1), 1994
Handle: RePEc:cwl:cwldpp:909r

Note: CFP 863.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Asymptotic results; bracketing method; empirical process; kernel estimator; nonparametric density estimator; nonparametric regression estimator; semiparametric estimator; semiparametric test; series expansion; Sobolev norm; stochastic equicontinuity;

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Cited by:
  1. 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.
  2. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, Econometric Society, vol. 64(6), pages 1263-97, November.
  3. Yoon-Jae Whang & Donald W.K. Andrews, 1991. "Tests of Specification for Parametric and Semiparametric Models," Cowles Foundation Discussion Papers 968, Cowles Foundation for Research in Economics, Yale University.
  4. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Density Estimators for Daily Volatility Based on the Use of Realized Measures," Departmental Working Papers 200620, Rutgers University, Department of Economics.

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