Malaria can be diagnosed by the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, however, an individual may have fever attributable either to malaria or to other causes. Thus the parasite level of an individual with fever follows a two-component mixture, with the two components corresponding to malaria and nonmalaria individuals. Furthermore, the parasite levels of nonmalaria individuals can be characterised as a mixture of a zero component and a positive distribution. In this article, we propose a nonparametric maximum multinomial likelihood approach for estimating the proportion of malaria using parasite-level data from two groups of individuals collected in two different seasons. We develop an EM-algorithm to numerically calculate the proposed estimates and further establish their convergence rates. Simulation results show that the proposed estimators are more efficient than existing nonparametric estimators. The proposed method is used to analyse malaria survey data.

可以通过寄生虫的存在和寄生虫引起的症状（通常是发烧）来诊断疟疾。但是，在流行地区，个人可能会因疟疾或其他原因而发烧。因此，发烧个体的寄生虫水平遵循两种成分的混合物，其中两种成分分别对应于疟疾和非疟疾个体。此外，非疟疾个体的寄生虫水平可以表征为零成分和正分布的混合物。在本文中，我们提出了一种非参数最大多项式似然方法，该方法使用了来自两个不同季节的两组个体的寄生虫水平数据来估计疟疾的比例。我们开发了一种EM算法，以数字方式计算建议的估算值，并进一步确定其收敛速度。仿真结果表明，所提出的估计器比现有的非参数估计器更有效。所提出的方法用于分析疟疾调查数据。