A0319
Title: Robust and efficient parameter estimation for discretely observed stochastic processes
Authors: Rohan Hore - University of Chicago (United States)
Abhik Ghosh - Indian Statistical Institute (India) [presenting]
Abstract: In various practical situations, data is encountered from stochastic processes, which can be efficiently modelled using an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference methods based on the maximum likelihood (ML) principle are susceptible to minor deviations from assumed model or data contamination due to their well-known lack of robustness. Since the alternative non-parametric procedures often lose significant efficiency, a robust parameter estimation procedure is developed for discretely observed data from a parametric stochastic process model, which exploits the properties of the popular density power divergence measure in the framework of minimum distance inference. In particular, the minimum density power divergence estimators (MDPDE) are defined for the independent increment and the Markov processes. The asymptotic consistency and distributional results are established for the proposed MDPDEs in these dependent stochastic process set-ups, and their benefits are illustrated over the usual ML estimator for common examples like the Poisson process, drifted Brownian motion and auto-regressive models.
