Analisi multivariata per osservazioni appaiate con dati mancanti: un caso studio

All parametric approaches require that analysis should be done on complete data sets and so, in presence of missing data, parametric solutions are based either on the so-called deletion principle or imputation methods. But when we delete incomplete vectors we also remove all information they contain, which may be valuable and useful for analysis. And when we replace missing data by suitable functions of actually observed data, that is imputing method, we may introduce biased information which may negatively infuence the analysis. On the other hand, non-parametric solutions in a permutation framework consider data as they are, and units with missing data participate in the permutation mechanism as well as all other units, without deletion or imputing. In this paper we provide a comparison between a parametric solution, represented by ITT principle, and a non parametric one, in a testing problem with multivariate paired observations

Nonparametric combination tests for comparing two survival curves with informative and non-informative censoring

This paper looks at permutation methods used to deal with hypothesis testing within the survival analysis framework. In the literature, several attempts have been made to deal with the comparison of survival curves and, depending on the survival and hazard functions of two groups, they can be more or less efficient in detecting differences. Furthermore, in some situations, censoring can be informative in that it depends on treatment effect. Our proposal is based on the nonparametric combination approach and has proven to be very effective under different configurations of survival and hazard functions. It allows the practitioner to test jointly on primary and censoring events and, by using multiple testing methods, to assess the significance of the treatment effect separately on the survival and the censoring process

Some hypothesis testing problems for categorical variables

This paper considers some testing problems for multivariate categorical variables within a conditional, or permutation, framework. The key idea is based on the decomposition of null and alternative hypotheses into a number of sub-hypotheses. For each sub-hypothesis it is assumed that a proper permutation partial test is available. Of course, these partial tests are assumed to be not independent. Then, the global testing solution is obtained by a nonparametric combination of resulting p-values. The theory of nonparametric combination and a computing algorithm to perform related calculations are outlined. As a particular result, a test analogous to Hotelling’s T2 for nominal and ordered categorical variables is obtained. Moreover, an analysis from the point of view of multiple testing is also outlined in order to inspect which variable or class or group is mostly responsible of a global significance

Tecniche di ricampionamento e verifica multidimensionale delle ipotesi

The paper deals with some multidimensional testing problems when the permutational principle applies. The proposed solutions are based on without replacement resampling techniques and nonparametrical combination of several dependent first order tests. In particular, a multidimensional extension of a permutational t-paired, a MANOVA with categorical and quantitative variables and a dominance test for ordered categorical variables are given. Moreover, problems implying some violations of the permutational principle, such as treatment of missing values and the multidimensional Behrens-Fisher, are also discussed

Some comments on the decision approach to statistical inference

The decision approach to statistical inference is discussed from the point of view of the aptitude of its underlying principles to be useful in the real problem solving area. Conditional and non conditional statistical decision inference are also discussed. Moreover a set of inferential problems for which the decision approach fails are examined. So that if a statistician wants to solve them he needs to have at his disposal a set of different inferential approaches, based on different underlying principles and/or axioms, useful in different situations and for different tasks. Therefore, in a complex problem, he could need many approaches at the same time, especially if this problem can be put into a set of inferential subproblems