We consider a unified description of classification rules for nearly singular covariance matrices. When the covariance matrices of the groups or the pooled covariance matrix become nearly singular, bayesian classification rules become seriously unstable. Several procedures have been proposed to...

We investigate the combination of the dimension reduction methods SIR (Li, 1991) and DAME (Gather et al., 2001) with fuzzy-clustering to validate a given classification. We consider certain economic variables which are assumed to contain the information relevant to determine the current phase of...

This paper analyses the influence of 13 stylized facts of the German economy on the West German business cycles from 1955 to 1994. The method used in this investigation is Statistical Experimental Design with orthogonal factors. We are looking for all existing Plackett-Burman designs realizable...

Linear Discriminant Analysis (LDA) performs well for classifica- tion of business phases even though the premises of an LDA are not met. As the variables are highly correlated there are numerical as well as interpretational shortcomings. By transforming the classification problem to a regression...

In this paper business cycles are considered as a multivariate phenomenon and not as a univariate one determined e.g. by the GNP. The subject is to look for the number of phases of a business cycle, which can be motivated by the number of clusters in a given dataset of macro-economic variables....

We propose a computer intensive method for linear dimension reduction which minimizes the classification error directly. Simulated annealing (Bohachevsky et al 1986) as a modern optimization technique is used to solve this problem effectively. This approach easily allows to incorporate user...