  We study sufficient conditions for local asymptotic mixed normality. We
weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhya Ser. A
1982) so that they can be applied to a wider class of statistical models
including a jump-diffusion model. Moreover, we show that local asymptotic mixed
normality of a statistical model generated by approximated transition density
functions is implied for the original model. Together with density
approximation by means of thresholding techniques, we show local asymptotic
normality for a statistical model of discretely observed jump-diffusion
processes where the drift coefficient, diffusion coefficient, and jump
structure are parametrized. As a consequence, the quasi-maximum-likelihood and
Bayes-type estimators proposed in Shimizu and Yoshida (Stat. Inference Stoch.
Process. 2006) and Ogihara and Yoshida (Stat. Inference Stoch. Process. 2011)
are shown to be asymptotically efficient in this model. Moreover, we can
construct asymptotically uniformly most powerful tests for the parameters.
