Statistical classification and curve estimation in some nonstandard cases

我的研究建议的主要部分涉及缺失数据的统计分类。统计分类长期以来一直被用作物理，生物和社会科学几乎所有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。感兴趣的特征，通常称为类别成员资格，总是一个分类/离散量，如健康或生病，正确或不正确，低或中或高，0或1等。 一个简单的例子是一个人被分类为患有某种类型的疾病的情况下，基于测量，如心跳，血压，年龄等，然后问题是找到一个分类器（一种功能）可以根据其相应的特征集尽可能最好地预测一个人的类别成员资格;这里的“最佳”是指具有最低可能的误分类错误率。我的研究建议的另一部分涉及存在缺失数据时的曲线估计问题。 这里，曲线可以是数据的潜在真实分布，也可能是回归曲线。这些曲线在统计推断领域有着广泛的应用。由于在实践中，许多真实的数据集都有缺失值，因此需要修改程序，以便有效地处理缺失数据。我坚信，我的研究结果是非常有用的，适用于统计科学的一般领域，并可以提供强有力的工具，各种加拿大研究（统计）社区。

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.