Estimation and Computation for Multivariate Classification and Mixture Problems

9802522Bernhard flury本研究侧重于多元统计中的分类方法，研究理论、实践和计算方面。研究者探索具有“不适当”成分的有限混合模型，即每个数据点具有相同密度值的成分。这就产生了一类灵活的依赖于调优参数设置的估计器。对于调谐参数的极值，所得到的估计方法分别对应于全参数最大似然和非参数似然（经验分布函数）。该估计器对污染数据很有用，并与传统的鲁棒估计器进行了性能比较。主要的计算工具是EM算法的一个应用。在与有限混合分析相关的另一个问题中，研究者研究了维度问题：如果兴趣集中在测量变量的子集上，是否应该仅使用该特定子集来估计混合参数，还是应该使用其余变量（“协变量”）？此外，本研究发展了多元模型中极大似然估计量的渐近分布理论，这些模型通常被认为是传统方法难以处理的（公正则变量，部分公主成分，判别子空间模型等），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、模式与语音识别、分类学等领域发挥着越来越重要的作用。研究者研究多元情况下的估计和计算方法，即在同一对象上测量许多变量时。特别是，在本研究中使用的有限混合模型使我们能够在数据被错误和异常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，并使其适用于许多领域的问题，包括生物技术和环境科学。进一步的研究课题包括生物学中的异速生长模型，改进无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，以及生物学中周期性现象的分析。

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.