Application of the maximum likelihood estimation for the searching of hidden nonlinear dependencies .

Buchnev O. S.

The problem of nonlinearity in data analysis is relevant for most statistical methods. Data analysis is useful, among other things, for reducing the dimension or for searching for hidden dependencies in data. For searching of hidden dependencies, factor analysis is used. The most powerful of factor analysis methods is the maximum likelihood estimation, and it is successfully used for searching of hidden linear relationships. But when the dependencies are nonlinear, the maximum likelihood estimation does not always give good results. In this paper a modification of the maximum likelihood estimation is proposed. In the proposed modification of the MLE, the pair correlation matrix is proposed to be replaced by the matrix of correlation indexes obtained by using polynomial regression. A method for converting the resulting matrix of correlation indexes into a symmetric matrix is proposed. The results of the modified MLE operation on both model and real data are presented. The proposed modification of the MLE can supplement the set of methods available to the researcher. The results of the modified MLE can provide additional information about the subject area in the analysis of data, including the search and study of hidden dependencies.

Keywords:factor analysis, maximum likelihood estimation, polynomial regression, correlation index, nonlinear dependence.