Mathematical Sciences: Mixture Analysis

数理统计的研究分为 三个部分：离散样本中过度分散的检验 分布，检验样本是否来自正态分布 分布而不是正态分布的有限混合 混合正态分布的半参数估计 密度的将构建一个新的测试， 混合物. 也是一个新的测试和诊断的数量 将导出混合物中的组分。为实现这些目标将 利用混合密度和未混合密度的比率的几何形状。 另一个目标是使用 方法，其中平滑参数通过交叉选择， 验证。

The research in mathematical statistics is divided into three parts: testing for overdispersion in discrete distributions, testing that a sample comes from a normal distribution rather than a finite mixture of normal distributions, and semi-parametric estimation of a mixed normal density. A new test will be constructed for the presence of a mixture. Also a new test and diagnostic for the number of components in a mixture will be derived. This will be achieved by exploiting the geometry of ratios of mixed and unmixed densities. A further goal is to estimate the mixed normal density using an approach in which a smoothing parameter is selected via cross- validation.