It is well known that in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with "sandwich" covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal and of asymptotic variance that is in general different than the sandwich matrix. It is shown that due to t...

This paper is devoted to the controlled drift estimation of mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one optimal input where we find function which maximize Fisher information for unknown parameter and other with a constant as function. Large sample asymptotical properties Maximum Likelihood Estimator (MLE) deduced using Laplace transform computations or Cameron...

Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements both in theory and in practice over the maximum likelihood estimator (MLE), particularly in high dimensional scenarios involving para...

In this thesis we study issues related to estimators behavior. We examine the general scalar measurement equation yn = h(θ) + vn, from which we wish to estimate the parameter θ. Specifically, we concentrate on problems where θ is a continuous parameter and the Fisher Information Measure (FIM) equal zero at isolated points θi. The well-known Cramér-Rao Lower Bound (CRLB) on the variance of any u...

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear pa...

We refine the general methodology in [1] for the construction and analysis of essentially minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions with support size S comparable with the number of observations n. Specifically, we determine the “smooth” and “non-smooth” regimes based on the confidence set and the smo...

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency o...

Fosdick and Raftery (2012) revisited the classical problem of inference for a bivariate normal correlation coefficient ρ when the variances are known. They considered several frequentist and Bayesian estimators, the former including the maximum likelihood estimator (MLE), but did not obtain the standard errors of these estimators or confidence intervals for ρ. Here we present a new variance-sta...

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable ...

We consider the problem of inference from multinomial data with chances θ, subject to the a-priori information that the true parameter vector θ belongs to a known convex polytope Θ. The proposed estimator has the parametrized structure of the conditional-mean estimator with a prior Dirichlet distribution, whose parameters (s, t) are suitably designed via a dominance criterion so as to guarantee...