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

[408158]董某：本文研究的目的是获得高维有序列联表的单元概率的投影跟踪估计。离散数据通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系。由每个类别的个体数目组成的表格是三维有序列联表。高维表单元格概率估计的难点在于缺乏数据。在具有10个类别的一维表中，100个观察值的样本的平均单元格计数为10，但是在每个维度中具有相同数量的类别的五维表中，它的平均单元格计数仅为0.001。所有现有的估计器都有一个共同的问题，即维度诅咒，这是由高维表中缺乏数据引起的。该研究通过观察不再稀疏的一维投影来研究高维数据的特征。一维表被定义为d维表沿任意方向的投影。引入了一个指标来评价预测结果。通过使用较小的平滑参数可以发现有趣的特征，而不会牺牲估计器的方差，从而克服了维数的问题。＊＊＊

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. ***