The efficiency of the MLE is demonstrated indirectly by using the following theorem. Theorem [7, p. ZSS]: If an estimator exists such that equality is satisfied in the Cramer-Rao inequality, it can be determined as a solution of the maximum likelihood equation. We will show that such an estimator exists. This implies that the covariance matrix of the MLE is given by the inverse of the Fisher in...

We consider the Cox proportional hazards model with discrete-valued covariates subject to misclassification. We present a simple estimator of the regression parameter vector for this model. The estimator is based on a weighted least squares analysis of weighted-averaged transformed Kaplan-Meier curves for the different possible configurations of the observed covariate vector. Optimal weighting ...

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability αα. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likeli...

In this paper we present a method for estimating population divergence times by maximum likelihood in models without mutation. The maximum-likelihood estimator is compared to a commonly applied estimator based on Wright's FST statistic. Simulations suggest that the maximum-likelihood estimator is less biased and has a lower variance than the FST -based estimator. The maximum-likelihood estimato...

Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Mar...

For the problem of estimating a regression function, μ say, subject to shape constraints, like monotonicity or convexity, it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. ...

This article considers random coefficient models (RCMs) for time-series–crosssection data. These models allow for unit to unit variation in the model parameters. The heart of the paper compares the finite sample properties of the fully pooled estimator, the unit by unit (unpooled) estimator and the (maximum likelihood) RCM estimator. The maximum likelihood estimator RCM performs well, even wher...

This article considers random coefficient models (RCMs) for time-series–cross-section data. These models allow for unit to unit variation in the model parameters. The heart of the article compares the finite sample properties of the fully pooled estimator, the unit by unit (unpooled) estimator, and the (maximum likelihood) RCM estimator. The maximum likelihood estimator RCM performs well, even ...

In this paper, the reliability formula of stress-strength model is derived for probability a component having strength X falling between two stresses T and Z, based on The New Weibull-Pareto Distribution with unknown parameter known common parameters . Four methods estimating are discussed which Maximum Likelihood, Method Moment, Least Square Weighted Method, comparison these estimations simula...

The logistic regression model is commonly used to describe the e,ect of one or several explanatory variables on a binary response variable. It su,ers from the problem that its parameters are not identi/able when there is separation in the space of the explanatory variables. In that case, existing /tting techniques fail to converge or give the wrong answer. To remedy this, a slightly more genera...