Statistical tests based on empirical processes

在大多数统计学应用中，随机动态模型被假定满足一定的假设，主要与它们的概率分布有关。例如，在时间序列中，通常假设随机误差项（创新）是独立的和/或具有属于某些参数族的密度。该研究计划的总体目标是进一步研究基于伪观测的经验过程，伪观测是对来自同一样本的数据进行转换，并利用它们对主要出现在精算科学、计量经济学和统计学中的模型进行变点检验、独立性检验和拟合优度检验。

In most applications of statistics, stochastic dynamic models are assumed to satisfy certain assumptions, mainly related to their probability distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a density belonging to some parametric family. The general objective of the proposed research program is to further study empirical processes based on pseudo-observations, which are transformations of data from the same sample, and use them to develop tests of change-point, independence and goodness-of-fit test for models appearing mainly in actuarial science, econometrics, and statistics.