  We prove the local asymptotic mixed normality (LAMN) property for a family of
probability measures defined by parametrized diffusion processes with
nonsynchronous observations. We assume that observation times of processes are
independent of processes and we will study asymptotics when the maximum length
of observation intervals goes to zero in probability. We also prove that the
quasi-maximum likelihood estimator and the Bayes-type estimator proposed in
Ogihara and Yoshida (Stochastic Process. Appl. 124 (2014) 2954-3008) are
asymptotically efficient.
