Empirical likelihood based inference for second-order diffusion models

Abstract

In this paper, we develop an empirical likelihood method to construct empirical likelihood estimators for nonparametric drift and diffusion functions in the second-order diffusion model, and the consistency and asymptotic normality of the empirical likelihood estimators are obtained. Moreover, the nonsymmetric confidence intervals for drift and diffusion functions based on empirical likelihood methods are obtained, and the adjusted empirical log-likelihood ratio is proved to be asymptotically standard chi-square under some mild conditions.