Mathematical Sciences: Mixture Analysis

数理统计的研究分为三个部分：离散分布的超离散度检验，样本来自正态分布而不是正态分布的有限混合的检验，以及混合正态密度的半参数估计。将对混合物的存在进行新的测试。此外，还将对混合物中的组份数量进行新的测试和诊断。这将通过利用混合密度和非混合密度比率的几何图形来实现。另一个目标是使用通过交叉验证选择平滑参数的方法来估计混合法线密度。

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.