統計数学セミナー
Seminar on Probability and Statistics 
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Seminar on Probability and Statistics Thursday October 18 2012 Tokyo 006 3:154:25 pm
QuasiBayesian analysis of nonparametric instrumental variables models
加藤 賢悟 / KATO, Kengo 広島大学大学院理学研究科数学専攻 / Department of Mathematics, Graduate School of Science, Hiroshima University Abstract This paper aims at developing a quasiBayesian analysis
of the nonparametric instrumental variables model, with a focus on the
asymptotic properties of quasiposterior distributions. In this paper,
instead of assuming a distributional assumption on the data generating
process, we consider a quasilikelihood induced from the conditional
moment restriction, and put priors on the functionvalued parameter.
We call the resulting posterior quasiposterior, which corresponds to
``Gibbs posterior'' in the literature. Here we shall focus on sieve
priors, which are priors that concentrate on finite dimensional sieve
spaces. The dimension of the sieve space should increase as the sample
size. We derive rates of contraction and a nonparametric Bernsteinvon
Mises type result for the quasiposterior distribution, and rates of
convergence for the quasiBayes estimator defined by the posterior
expectation. We show that, with priors suitably chosen, the
quasiposterior distribution (the quasiBayes estimator) attains the
minimax optimal rate of contraction (convergence, respectively). These
results greatly sharpen the previous related work.

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