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 ...

Large survey data are often accompanied by sampling weights that reflect the inequality probabilities for selecting samples in complex sampling. Sampling weights act as an expansion factor that, by scaling the subjects, turns the sample into a representative of the community. The quasi-maximum likelihood method is one of the approaches for considering sampling weights in the frequentist framewo...

We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maxim...