Nakahiro YOSHIDA- Abstract

POLYNOMIAL TYPE LARGE DEVIATION INEQUALITY FOR A STATISTICAL RANDOM FIELD AND ITS APPLICATIONS

Nakahiro YOSHIDA

University of Tokyo
Tokyo, Japan

ABSTRACT

Recently Kutoyants (2003, Springer) presented a polynomial type large deviation inequality (PLDI) for a parametric model of a diffusion process by means of the local time. We will give a PLDI for a statistical random field associated with an $M$-estimator, by modifying the proof of the weak convergence of a random field in Yoshida (1990, AISM). We also discuss applications to inference for stochastic differential equations with/without jumps based on continuous/discrete observations