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The bootstrap and the Edgeworth correction for semiparametric averaged derivatives

Nishiyama, Yoshihiko and Robinson, Peter M. (2005) The bootstrap and the Edgeworth correction for semiparametric averaged derivatives. Econometrics; EM/2005/483, EM/05/483. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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Identification Number: EM/05/483

Abstract

In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of interest, especially in sample sizes that are not enormous. We show that a bootstrap distribution achieves a valid Edgeworth correction in case of density-weighted averaged derivative estimates of semiparametric index models. Approaches to bias-reduction are discussed. We also develop a higher order expansion, to show that the bootstrap achieves a further reduction in size distortion in case of two-sided testing. The finite sample performance of the methods is investigated by means of Monte Carlo simulations from a Tobit model.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2005 Yoshihiko Nishiyama and Peter M. Robinson
Subjects: H Social Sciences > HB Economic Theory
JEL classification: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods
C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C24 - Truncated and Censored Models
Sets: Collections > Economists Online
Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Date Deposited: 27 Apr 2007
Last Modified: 01 Oct 2010 08:47
URI: http://eprints.lse.ac.uk/id/eprint/2297

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