Local asymptotic mixed normality property for nonsynchronously observed diffusion processes

Abstract

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.

Published at http://dx.doi.org/10.3150/14-BEJ634 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes
• Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency
• Quasi-Likelihood Analysis for Stochastic Regression Models with Nonsynchronous Observations

Cited by in corpus (1)

• Local Asymptotic Mixed Normality via Transition Density Approximation and an Application to Ergodic Jump-Diffusion Processes