We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positive-part JamesStein estimator under the choice of an uninformative prior. A new approach for estimating parameters and hyperparameters in general hierarchical Bayes mod...

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for change-point dates in linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998, Econometrica 66, 47–78). The GL estimator is defined by an integration rather than optimization-based method relies on LS criterion function. It...

The naive importance sampling estimator based on the samples from a single importance density can be extremely numerically unstable. We consider multiple distributions importance sampling estimators where samples from more than one probability distributions are combined to consistently estimate means with respect to given target distributions. These generalized importance sampling estimators pr...

The use of Mathematica in deriving mean likelihood estimators is discussed. Comparisons are made between the mean likelihood estimator, the maximum likelihood estimator, and the Bayes estimator based on a Jeffrey’s noninformative prior. These estimators are compared using the mean-square error criterion and Pitman measure of closeness. In some cases it is possible, using Mathematica, to derive ...