Efficient estimation for semiparametric models by reproducing kernel Hilbert space

A semiparametric model is a class of statistical models, which are characterized by a finite dimensional parameter and an infinite dimensional parameter. Asymptotic variance of estimator of the finite dimensional parameter is minimized when semiparametric efficient estimation is implemented. However, the efficient estimation is not possible for some models. We suggest a general method to carry out the efficient estimation for wide range of semiparametric models. Our method adopt a theory of reproducing kernel Hilbert space. Based on the theory, we represent an operator to a linear space of score function, and it enables us to implement the efficient estimation. We also provide theory of consistency of our method, and some numerical experiments. ∗I would like to express my deepest gratitude to Katsumi Shimotsu who provided helpful comments and suggestions. I also owe a very important debt to Yoichi Nishimura, Kengo Kato and Yukitoshi Matsushita whose meticulous comments were an enormous help to me. I would also like to express my gratitude to my family for their moral support and warm encouragements. Finally, I gratefully appreciate the financial support of GSDM project that made it possible to complete our research. The responsibility of any errors is of course mine.