Model and method for analysis of categorical data with relations [Abstract of thesis]
We introduce new estimates and tests of independence in copula models with unknown margins using -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of -divergence has good properties in terms of efficiency-robustness.
The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.
Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.
The problem is to determine the optimum size of nonsensitiveness regions for the level of statistical tests. This is closely connected with the problem of the distribution of quadratic forms.