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The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives*
Author(s) -
Nishiyama Yoshihiko,
Robinson Peter M.
Publication year - 2005
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2005.00598.x
Subject(s) - edgeworth series , mathematics , smoothing , semiparametric model , parametric statistics , monte carlo method , tobit model , semiparametric regression , statistics , econometrics
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 the 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 the case of two‐sided testing. The finite‐sample performance of the methods is investigated by means of Monte Carlo simulations from a Tobit model.