Mathematical Sciences: Problems in Mathematical Statistics

研究将进行数据驱动的平滑参数选择和评估非参数曲线估计器的可变性。本文将研究序列分析中的自由边界问题，特别是一般先验问题的方法。将尝试建立一个关于“轰炸机问题”（关于防御分配率）的猜想。对估计失真的一般问题的初步研究将应用于加密。在数据网格被未知的自然边界分割成两组数据的情况下，将研究一种估计边界的非参数方法。为了处理依赖观测值和重尾观测值，将研究对bootstrap的修改，这是一种用于模拟统计量抽样分布的非参数技术。

Research will be conducted on data-driven smoothing parameter selection and assessment of the variability of nonparametric curve estimators. Methodology will be developed for the free boundary problem in sequential analysis, particularily for general priors. Attempts will be made to establish a conjecture for the "bomber problem" (concerning defense allocation rates). A pilot study for the general problem of estimating distortion will be applied to encryption. In the case that a grid of data is partitioned by an unknown natural boundary that separates data into two homogeneous groups, a nonparametric method for estimating the boundary will be studied. To deal with dependent observations and heavy-tailed observations, research will be carried out on modifications of the bootstrap, a nonparametric technique for modelling the sampling distribution of a statistic.