統計学輪講（第８回）

日時      2006年 5月 30日(火)    15時〜16時40分
場所      経済学部新棟３階第２教室
講演者    市村 英彦(経済)
演題      Characterization of the Asymptotic Distribution of Semiparametric
          M-Estimators

概要
This paper develops a concrete formula for the asymptotic distribution
of two-step, possibly non-smooth semiparametric M-estimators
under general misspecification.  Our regularity conditions are
relatively straightforward to verify
and also weaker than those available in the literature.

The first-stage nonparametric estimation may depend on finite
dimensional parameters.

We characterize:
(1) conditions under which the first-stage estimation of nonparametric
components do not affect the asymptotic distribution,
(2) conditions under which the asymptotic distribution is affected by
the derivatives of the first-stage nonparametric estimator
with respect to the finite-dimensional parameters, and
(3) conditions under which one can allow non-smooth objective functions.

Our framework is illustrated by applying it to three examples:
(1) profiled estimation of a single index quantile regression model,
(2) semiparametric least squares estimation under model
misspecification, and
(3) a smoothed matching estimator.

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Tokyo University