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THE INTEGRATED MEAN SQUARED ERROR OF SERIES REGRESSION AND A ROSENTHAL HILBERT-SPACE INEQUALITY

Published online by Cambridge University Press:  19 August 2014

Bruce E. Hansen
Bruce E. Hansen*
Affiliation:
University of Wisconsin
*
*Address correspondence to Bruce Hansen, Department of Economics, University of Wisconsin-Madison, 1180 Observatory Drive, Madison, WI 53706, USA; e-mail: behansen@wisc.edu. www.ssc.wisc.edu/∼bhansen.
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Abstract

This paper develops uniform approximations for the integrated mean squared error (IMSE) of nonparametric series regression estimators, including both least-squares and averaging least-squares estimators. To develop these approximations, we also generalize an important probability inequality of Rosenthal (1970, Israel Journal of Mathematics 8, 273–303; 1972, Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 149–167. University of California Press) to the case of Hilbert-space valued random variables.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 2: Haavelmo Memorial Issue: Part Two , April 2015 , pp. 337 - 361
Copyright
Copyright © Cambridge University Press 2014 

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