## Seminar on Probability and Statistics

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

### 2012/10/18

15:15-16:25   Room #006 (Graduate School of Math. Sci. Bldg.)
KATO, Kengo (Department of Mathematics, Graduate School of Science, Hiroshima University)
Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)
[ Abstract ]
This paper aims at developing a quasi-Bayesian analysis
of the nonparametric instrumental variables model, with a focus on the
asymptotic properties of quasi-posterior distributions. In this paper,
instead of assuming a distributional assumption on the data generating
process, we consider a quasi-likelihood induced from the conditional
moment restriction, and put priors on the function-valued parameter.
We call the resulting posterior quasi-posterior, 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 non-parametric Bernstein-von
Mises type result for the quasi-posterior distribution, and rates of
convergence for the quasi-Bayes estimator defined by the posterior
expectation. We show that, with priors suitably chosen, the
quasi-posterior distribution (the quasi-Bayes estimator) attains the
minimax optimal rate of contraction (convergence, respectively). These
results greatly sharpen the previous related work.
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html