Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Uncertainty and Fuzzy Sets: Classifying the Situation

The so called “Plural Uncertainty Model” is considered, in which statistical, maxmin, interval and Fuzzy model of uncertainty are embedded. For the last case external and internal contradictions of the theory are investigated and the modified definition of the Fuzzy Sets is proposed to overcome the troubles of the classical variant of Fuzzy Subsets by L. Zadeh. The general variants of logit- and probit- regression are the model of the modified Fuzzy Sets. It is possible to say about observations within the modification of the theory. The conception of the “situation” is proposed within modified Fuzzy Theory and the classifying problem is considered. The algorithm of the classification for the situation is proposed being the analogue of the statistical MLM(maximum likelihood method). The example related possible observing the distribution from the collection of distribution is considered.

About the Concept of Weights of WLTE(k) Estimators

2002 Mathematics Subject Classification: 62F35, 62F15.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a Monte-Carlo Study

2000 Mathematics Subject Classification: Primary 62F35; Secondary 62P99

Study on Robustness of Strehler-Mildvan Model

2000 Mathematics Subject Classi cation: 62F35, 62F15

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.