Extends the maximum entropy information-theoretic density estimation method to provide a technique which guarantees that the resulting density is unimodal. The method inputs data in the form of moment or quantile constraints and consequently can handle both data-derived and non-data-derived information.>

The minimum cross entropy spectral analysis procedure (a generalization of maximum entropy spectral analysis) is formulated as a convex programming problem, and its unconstrained dual convex programming problem is shown. In this dual setting the Lagrange multipliers are precisely the dual variables, and the numerical solution values are easily determined by any of a number of nonlinear programming codes. This result vastly simplifies the computation of all such spectral density estimates.

Two important problems in the analysis of categorical questionnaire data are considered: assessment of question worth and variable selection, and discrete discriminant analysis when the data is nonordinal with many states and few respondents. The unifying approach used throughout is the concept of information theoretic distance measures. Simulations and applications to real data are presented.