ADAPTIVE ESTIMATION OF DISTRIBUTIONS USING EXPONENTIAL SUB-FAMILIES

An algorithm is presented that, for a large-dimensional exponential fa mily G, finds a lower dimension exponential sub-family of G which cont ains distributions best fitting groups of identically distributed obse rvations within a set of data. The data are therefore fitted to a fami ly of distributions that has been adaptively chosen as representative of them. The algorithm is implemented in the special case in which G i s a logspline family of distributions. An example data set is analyzed using the method.