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



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