Search results for "Multivariate normal distribution"
showing 7 items of 47 documents
Regression models for multivariate ordered responses via the Plackett distribution
2008
AbstractWe investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear e…
Adaptive designs with correlated test statistics
2009
In clinical trials, the collected observations such as clustered data or repeated measurements are often correlated. As a consequence, test statistics in a multistage design are correlated. Adaptive designs were originally developed for independent test statistics. We present a general framework for two-stage adaptive designs with correlated test statistics. We show that the significance level for the Bauer-Köhne design is inflated for positively correlated test statistics from a bivariate normal distribution. The decision boundary for the second stage can be modified so that type one error is controlled. This general concept is expandable to other adaptive designs. In order to use these de…
Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores
1994
After some discussion of the purposes of testing multivariate normality, the paper concentrates on two different approaches to testing linearity: on repeated regression tests of non-linearity and on exploiting properties of a dichotomized normal distribution. Regression tests of linearity are used to examine the adequacy of linear scoring systems for explanatory variables, initially recorded on an ordinal scale. Examples from recent psychological and medical research are given in which the methods have led to some insight into subject-matter.
Affine equivariant multivariate rank methods
2003
The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. …
An approximation to maximum likelihood estimates in reduced models
1990
SUMMARY An approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model, i.e. a model with additional parameters. The approximation is close provided that the data are consistent with the first model. Applications are described to log linear models for discrete data, to models for multivariate normal distributions with special covariance matrices and to mixed discrete-continuous models.
Two ways to handle dependent uncertainties in multi-criteria decision problems☆
2009
Abstract We consider multi-criteria group decision-making problems, where the decision makers (DMs) want to identify their most preferred alternative(s) based on uncertain or inaccurate criteria measurements. In many real-life problems the uncertainties may be dependent. In this paper, we focus on multicriteria decision-making (MCDM) problems where the criteria and their uncertainties are computed using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. The simulation model determines for the criteria a joint probability distribution, which quantifies the uncertainties and their dependencies. We present and compare two…
Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach
2011
In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.