9408158 Dong The purpose of the proposed research is to obtain a projection pursuit estimator for cell probabilities of high-dimensional ordered contingency tables. Discrete data often appear in the form of contingency tables. For instance, consider the association among smoking statuses, age and breathing test results. A table consisting of the number of individuals in each category is a three-dimensional ordinal contingency table. The difficulty of estimating cell probability of high-dimensional tables is the lack of data. A sample of 100 observations in a one-dimensional table with 10 categories has an average cell count of 10, but it only has an average cell count of 0.001 in a five-dimensional table with the same number of categories in each dimension. All the existing estimators share a common problem known as the curse of dimensionality, which is caused by the lack of data in high-dimensional tables. The proposed research studies the features of high-dimensional data by looking at its one-dimensional projections, which are no longer sparse. A one-dimensional table is defined as a projection of a d-dimensional table along an arbitrary direction. An index is introduced to evaluate the projections. Interesting features can be uncovered by using smaller smoothing parameters without sacrificing the variance of the estimator -hus overcoming the problem of the curse of dimensionality. ***
