Estimation and Computation for Multivariate Classification and Mixture Problems

本研究侧重于多元统计中的分类方法，从理论、实践和计算三个方面进行研究。研究人员探索了具有“不适当”分量的有限混合模型，即每个数据点具有相同密度值的分量。这导致了一类灵活的估计器，其依赖于调节参数的设置。对于调谐参数的极值，所得到的估计方法分别对应于完全参数极大似然和非参数似然(经验分布函数)。这种估计器对污染数据很有用，其性能与传统的稳健估计器进行了比较。主要的计算工具是EM算法的应用。在与有限混合分析有关的另一个问题中，研究人员研究了维度问题：如果人们的兴趣集中在测量的变量子集上，是否应该只使用该特定子集来估计混合物的参数，还是应该也使用其余变量(“协变量”)？此外，本研究发展了通常被常规方法视为不可处理的多变量模型(公共规范变量、部分公共主成分、区分子空间模型等)中极大似然估计的渐近分布理论，并研究了估计其参数所需的迭代计算方法。分类方法在遥感、模式和语音识别以及分类等领域中发挥着越来越重要的作用。研究人员研究了多变量情况下的估计和计算方法，即在同一对象上测量多个变量的情况。特别是，这项研究中使用的有限混合模型允许我们在数据被误差和离群值扭曲的情况下改进统计方法。在这项研究中开发的高效计算方法使我们能够利用这一强大的方法，并使其适用于包括生物技术和环境科学在内的许多领域的问题。进一步的研究主题包括生物异速生长模型、改进的非监督分类方法的估计、为最近创建的多变量数据分析方法开发有效的计算算法，以及分析生物学中的周期性现象。

9802522Bernhard FluryThis research focuses on methods of classification in multivariate statistics, studying theoretical, practical, and computational aspects. The investigator explores finite mixture models with an "improper" component, i.e., a component in which each data point has the same density value. This leads to a flexible class of estimators that depend on the setting of a tuning parameter. For the extreme values of the tuning parameter, the resulting methods of estimation correspond to fully parametric maximum likelihood, and to nonparametric likelihood (empirical distribution function), respectively. The estimators are useful for contaminated data, and their performance is compared to traditional robust estimators. The main computational tool is an application of the EM algorithm. In another problem related to finite mixture analysis the investigator studies the question of dimensionality: if interest focuses on a subset of variables measured, should one use only that particular subsetfor the purpose of estimating the parameters of the mixture, or should one use the remaining variables ("covariates") as well? In addition, this research develops the asymptotic distribution theory for maximum likelihood estimators in multivariate models that are usually regarded as untractable by conventional methods (common canonical variates, partial common principal components, the discrimination subspace model, and others), and investigates iterative computational methods needed for estimating their parameters.Methods of classification play an increasingly important role in areas such as remote sensing, pattern and speech recognition, and taxonomy. The investigator studies methods of estimation and computation in multivariate situations, i.e., when many variables are measured on the same objects. In particular, the finite mixture model used in this research allows us to improve statistical methodology in situations where the data is distorted by errors and outliers. Efficient computational methods developed in this research allow us to exploit this powerful methodology, and to make it applicable to problems in many areas, including biotechnoloy and environmental sciences. Further research topics involve models of allometric growth in biology, improved estimation in unsupervised methods of classification, the development of efficient computational algorithms for recentlycreated multivariate methods of data analysis, and the analysis of periodic phenomena in biology.