Statistical classification and curve estimation in some nonstandard cases

我的研究计划的主要部分是在缺少数据的情况下进行统计分类。统计分类长期以来一直被用作几乎所有物理、生物和社会科学领域的主要决策程序。它是基于实体的其他特征来预测与实体相关的兴趣特征。兴趣的特征通常被称为类隶属度，它总是一个绝对的/离散的量，如健康或疾病、正确或不正确、低或中或高、0或1等。特征集通常是数值的有限集合。一个简单的例子是，根据心跳、血压、年龄等测量数据，将一个人归类为患有某种疾病。接下来的问题是找到一个分类器（一个函数），它可以根据相应的特征集尽可能地预测一个人的类隶属度；这里的“最佳”是指具有尽可能低的误分类错误率。我的研究计划的另一部分涉及在缺失数据存在下的曲线估计问题。在这里，曲线可能是数据的真实分布，也可能是回归曲线。这些曲线在统计推断领域有广泛的应用。由于在实践中，许多真实的数据集都有缺失值，因此需要修改过程，以有效地处理缺失数据。我坚信我的结果在统计科学的一般领域是非常有用和适用的，并且可以为各种加拿大研究（统计）社区提供强大的工具。

The main part of my research proposal involves statistical classification in the presence of missing data. Statistical classification has long been used as a major decision making procedure in almost all areas of physical, biological, and social sciences. It is about predicting a characteristic of interest associated with an entity based on the entity's other features. The characteristic of interest, which is usually called the class membership, is always a categorical/discrete quantity such as healthy or ill, correct or incorrect, low or medium or high, 0 or 1, etc. The feature set is typically a finite collection of numerical values.  A simple example is the case where a person is to be classified as having a certain type of illness, based on measurements such as heart-beats, blood pressure, age, etc. The problem is then to find a classifier (a function) that can predict the class membership of a person, based on its corresponding feature set, as best as possible; here "best" means having the lowest possible misclassification error rate.Another part of my research proposal deals with the problem of curve estimation in the presence of missing data.  Here, a curve may be the underlying true distribution of the data or perhaps a regression curve. These curves have extensive applications in the field of statistical inference.Since, in practice, many real data sets have missing values, one needs to have modified procedures that can deal with missing data in an effective way. I strongly believe that my results are very useful and applicable in the general area of Statistical Sciences, and can provide powerful tools to various Canadian research (statistical) communities.