Mathematical Sciences: A Projection Pursuit Estimator for Ordinal Contingency Table Cell Probabilities

小行星9408158 提出的研究的目的是获得一个投影寻踪估计单元概率的高维有序列联表。 离散数据经常以列联表的形式出现。 例如，考虑吸烟状况，年龄和呼吸测试结果之间的关联。 由每个类别中的个体数组成的表是三维有序列联表。 估计高维表的单元概率的困难在于数据的缺乏。 在一个包含10个类别的一维表中，一个包含100个观察值的样本的平均单元数为10，但在一个每个维度的类别数相同的五维表中，它的平均单元数仅为0.001。所有现有的估计器都有一个共同的问题，即维度灾难，这是由高维表中缺乏数据引起的。该研究通过查看不再稀疏的一维投影来研究高维数据的特征。 一维表定义为d维表沿沿着任意方向的投影。 引入了一个指标来评价预测结果。 有趣的功能，可以发现使用较小的平滑参数，而不牺牲方差的估计-HUS克服的问题的灾难的维数。 ***

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. ***