Statistical classification and curve estimation in some nonstandard cases

我的研究建议的主要部分涉及在存在缺失数据的情况下的统计分类。长期以来，统计分类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。它是关于基于实体的其他特征来预测与实体相关联的感兴趣的特征。通常被称为类成员资格的感兴趣的特征总是一个范畴/离散量，例如健康或生病、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，一个人基于诸如心跳、血压、年龄等测量被分类为患有某种疾病。然后问题是找到一个分类器(一个函数)，该分类器可以基于其相应的特征集尽可能好地预测一个人的类别成员；在这里，“最佳”意味着具有最低的可能的错误分类错误率。

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.