Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association... Show moreDistance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model. Show less
According to the minimum description length (MDL) principle, data compression should be taken as the main goal of statistical inference. This stands in sharp contrast to making assumptions about an... Show moreAccording to the minimum description length (MDL) principle, data compression should be taken as the main goal of statistical inference. This stands in sharp contrast to making assumptions about an underlying ``true'' distribution generating the data, as is standard in the traditional frequentist approach to statistics. If the MDL premise of making data compression a fundamental notion can hold its ground, it promises a robust kind of statistics, which does not break down when standard, but hard to verify, assumptions are not completely satisfied. This makes it worthwhile to put data compression to the test, and see whether it really makes sense as a foundation for statistics. A natural starting point are cases where standard MDL methods show suboptimal performance in a traditional frequentist analysis. This thesis analyses two such cases. In the first case it is found that although the standard MDL method fails, data compression still makes sense and actually leads to the solution of the problem. In the second case we discuss a modification of the standard MDL estimator that has been proposed in the literature, which goes against its data compression principles. We also review the basic properties of R_nyi's dissimilarity measure for probability distributions. Show less
