This paper revisits the classical inference results for profile quasi maximum likelihood estimators (profile MLE) in the semiparametric estimation problem. We mainly focus on two prominent theorems: the Wilks phenomenon and Fisher expansion for the profile MLE are stated in a new fashion allowing finite samples and model misspecification. The method of study is also essentially different from t...

This module introduces the maximum likelihood estimator. We show how the MLE implements the likelihood principle. Methods for computing th MLE are covered. Properties of the MLE are discussed including asymptotic e ciency and invariance under reparameterization. The maximum likelihood estimator (MLE) is an alternative to the minimum variance unbiased estimator (MVUE). For many estimation proble...

We study a class of quadratic stochastic programs where the distribution of random variables has unknown parameters. A traditional approach is to estimate the parameters using a maximum likelihood estimator (MLE) and to use this as input in the optimization problem. For the unconstrained case, we show that an estimator that shrinks the MLE towards an arbitrary vector yields a uniformly better r...

This paper develops a simple and computationally efficient parametric approach to the estimation of general hidden Markov models (HMMs). For non-Gaussian HMMs, computation maximum likelihood estimator (MLE) involves high-dimensional integral that has no analytical solution can be difficult accurately. We develop new alternative method based on theory estimating functions deconvolution strategy....

A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after s...

The error bound in probability between the approximate maximum likelihood estimator AMLE and the continuous maximum likelihood estimator MLE is investigated for nonlinear nonhomogenous stochastic system with unknown parameter. The rates of convergence of the approximations for Itô and ordinary integral are introduced under some regular assumptions. Based on these results, the in probability rat...

In the first part of this lecture, we will deal with the consistency and asymptotic distribution of maximum likelihood estimator. The second part of the lecture focuses on signal estimation/tracking. An estimator is said to be consistent if it converges to the quantity being estimated. This section speaks about the consistency of MLE and conditions under which MLE is consistent.

In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change...

The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) is given on two non-negative coefficients. Furthermore, improvement on the UE of the reciprocal of each scale parameter is also obtained un...