Statistical tests based on empirical processes

在统计学的大多数应用中，动态随机模型被假定满足某些假设，主要与它们的概率分布有关。例如，在时间序列中，随机误差项(新息)通常被假定为独立的和/或具有属于某个分布族的分布。拟议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的转换，并使用它们来对主要出现在精算学、计量经济学、金融工程和统计学中的模型进行不匹配测试。由于许多重要决定依赖于模型假设，拟议的研究项目将主要用于开发新的工具，以严格验证这些假设，从而做出更好的决定。

In most applications of statistics, dynamical stochastic models are assumed to satisfy certain hypotheses, mainly related to their probabilistic distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a distribution belonging to some family of distributions. 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 lack-of-fit for models appearing mainly in actuarial science, econometrics, financial engineering and statistics. Since many important decisions rely on model assumptions, the proposed research project will mainly be used to develop new tools to verify rigorously these assumptions and therefore make better decisions.