RAPALLO F

In this paper, we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to specify the notions of outlier and pattern of outliers. The language and some techniques from Algebraic Statistics are essential tools to make the...

Toric models have been recently introduced in the analysis of statistical models for categorical data. The main improvement with respect to classical log-linear models is shown to be a simple representation of structural zeros. In this paper we analyze the geometry of toric models, showing that a toric model is the disjoint union of a number of...

The Diaconis-Sturmfels algorithm is a method for sampling from conditional distributions, based on the algebraic theory of toric ideals. This algorithm is applied to categorical data analysis through the notion of Markov basis. An application of this algorithm is a non-parametric Monte Carlo approach to the goodness of fit tests for contingency...

In recent years, a method for sampling from conditional distributions for categorical data has been presented by Diaconis and Sturmfels. Their algorithm is based on the algebraic theory of toric ideals which are used to create so called "Markov Bases". The Diaconis-Sturmfels algorithm leads to a non-asymptotic Monte Carlo Markov Chain algorithm...

In this paper we apply the elimination technique to the computation of Markov bases, paying special attention to contingency tables with structural zeros. An algebraic relationship between the Markov basis for a table with structural zeros and the corresponding complete table is proved. In order to find the relevant Markov basis, it is enough...

In questo lavoro presentiamo un algoritmo per l'inferenza esatta sull'indice kappa di Cohen nel caso multivariato. Tale algoritmo è basato su tecniche di Algebra Commutativa che permettono di campionare efficientemente dallo spazio delle tabelle di contingenza multidimensionali con margini fissati. Forniamo inoltre alcune osservazioni sulla...

The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations is less than the number of variables. This situation is common situation in experiments with DNA...

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In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. It is known that in this case one has to compute universal Gröbner bases, and this is often infeasible also in small- and medium-sized problems. Here we focus on bounded two-way contingency tables under independence model. We...

In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization...

In this paper we study a new class of statistical models for contingency tables. We define this class of models through a subset of the binomial equations of the classical independence model. We prove that they are log-linear and we use some notions from Algebraic Statistics to compute their sufficient statistic and their parametric...

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This paper deals with the convergence in Mallows metric for classical multivariate kernel distribution function estimators. We prove the convergence in Mallows metric of a locally orientated kernel smooth estimator belonging to the class of sample smoothing estimators. The consistency follows for the smoothed bootstrap for regular functions of...

Given an undirected graph G, we define a new object H-G , called the mp-chart of G, in the max-plus algebra. We use it, together with the max-plus permanent, to describe the complexity of graphs. We show how to compute the mean and the variance of H-G in terms of the adjacency matrix of G and we give a central limit theorem for H-G . Finally,...