Semiparametric Efficient Estimation by Reproducing Kernel Hilbert Space

• Activity Number: 262
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Masaaki Imaizumi*
• Companies: The University of Tokyo
• Keywords: semiparametric model ; semiparametric efficient esitmation ; reproducing kernel Hilbert space

Abstract

A semiparametric model is a class of statistical models, which are characterized by a finite dimensional parameter and an infinite dimensional parameter. In many cases, we are interested in an estimator of the finite dimensional parameter. A semiparametric efficient estimation is an estimation which can minimize variance of asymptotic distribution of the estimator. The efficient estimation is not possible for some models, when a projection operator for the efficient estimation does not have analytical form. We suggest a general method to implement the semiparametric efficient estimation by representing the projection operator by reproducing kernel. Our proposed method does not restrict how the nonparametric parameter is estimated, thus our method can implement the efficient estimation for wide range of semiparametric models. We also prove consistency of our method, and some numerical experiments.