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.

For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern is focused on searching for methods to solve the high degree polynomial without using iterative approximation. An explicit estimator based on the Law of Lar...

It is well known that the normal mixture with unequal variance has unbounded likelihood and thus the corresponding global maximum likelihood estimator (MLE) is undefined. One of the commonly used solutions is to put a constraint on the parameter space so that the likelihood is bounded and then one can run the EM algorithm on this constrained parameter space to find the constrained global MLE. H...

The Maximum Likelihood Estimator (MLE) has commonly been used to estimate the unknown parameters in the finite mixture of distributions via the expectationmaximization (EM) algorithm. However, the MLE can be very sensitive to outliers in the data. Various approaches that have incorporated robustness in fitting mixtures and clustering are discussed. Special attention is given to the Weighted Tri...

We present an improved version of random projections that takes advantage of marginal norms. Using a maximum likelihood estimator (MLE), marginconstrained random projections can improve estimation accuracy considerably. Theoretical properties of this estimator are analyzed in detail.

An exponentiated Pareto distribution is defined. We then consider maximum likelihood estimator (MLE) of the threshold parameter β with known parameters α and c for the exponentiated Pareto distribution in (2.1) and then obtain the MLE of the tail-probability of the exponentiated Pareto distribution. Finally, we consider MLE of reliability in two independent exponentiated Pareto distributions.

In this paper, we derive the recurrence relations for the moments of function of single and two order statistics from Lindley distribution. We also consider the maximum likelihood estimation (MLE) of the parameter of the distribution based on multiply type-II censoring. The maximum likelihood estimator is comupted numerically because it does not have an explicit form for the parameter. Then, a ...

The uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) are derived for samples from uniform distribution in the presence of outliers, where outliers are generated from generalized uniform distribution (GUD), when one parameter of the GUD is known. In this case it has been shown that UMVUE is better than MLE. When both the parameters are unknown then...

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a non-existent MLE. Our conditions focus on the role of sampling zeros in the observed tabl...