The paper is concerned with estimation of the probability function of a discrete random variable by minimizing the Shannon quasi-norm while meeting the moment conditions for the probability function estimated. After describing this method in detail, the paper further focuses on deriving confidence intervals for probabilities and possible application of these methods to particular data sets. and Obsahuje seznam literatury
We combined mitochondrial (cyb, control region, coi, nd4) and nuclear (irbp, ghr, sry, lcat) DNA sequence data to infer phylogenetic relationships of arvicoline voles. The concatenated supermatrix contained 72.8 % of missing data. From this dataset, Bayesian inference showed close relationships of Arvicola and Chionomys, Proedromys with Lasiopodomys and Microtus gregalis, Phaiomys with Neodon and M. clarkei. Genus Microtus formed a supported group with Blanfordimys and N. juldaschi. The gene partition taxon sets were explained in the multilocus phylogeny in such a way that the resulting Bayesian inference tree represented a unique solution on a terrace in the tree space. This means that although the supermatrix contained a large proportion of missing data, it was informative in retrieving a phylogeny with a unique optimality score, tree likelihood.
This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced
\begin{enumerate} \item[(i)] by Liese and Vajda \cite{9} and independently Broniatowski and Keziou \cite{3}, called here \textsl{power superdivergence estimators, } \item[(ii)] by Broniatowski and Keziou \cite{4} , called here \textsl{power subdivergence estimators, } \item[(iii)] by Basu et al. \cite{2}, called here \textsl{power pseudodistance estimators, }and \item[(iv)] by Vajda \cite{18} called here \textsl{Rényi pseudodistance estimators.} \end{enumerate}
These various criterions have in common to eliminate all need for grouping or smoothing in statistical inference. The paper studies and compares general properties of these estimators such as Fisher consistency and influence curves, and illustrates these properties by detailed analysis of the applications to the estimation of normal location and scale.