本项目主要研究函数型数据的检验及其相关问题，该问题是统计学研究的前沿和核心问题之一，在医学、生物、经济和能源等领域具有十分重要的应用价值。虽然目前该领域取得了一些成果，但由于研究方法的局限性，导致研究成果难于应用。如何结合实际应用背景，创新研究方法，使得该领域的研究成果取得更大的突破，是本项目追求的目标。本项目研究内容是研究函数回归模型的相依关系的检验问题；相依函数数据模型及阶数检验问题；多元函数数据关系的检验问题。最后，将检验方法应用到实际问题中去。本项目主要目的是通过克服已有检验方法的缺陷，提出新的检验方法，获得新的结果来丰富检验理论。同时，又为实际应用提供理论依据和指导。

This project mainly focuses on hypothesis testing based on functional data, which is one of the frontier and the core problem in statistical research, has very important value in medicine, biology, economy and energy and other fields. Although some achievements had been made in this area, but due to the limitations of the research methods, research results in this area are difficult to apply. The goal of this project is that proposed some new research methods which have made a breakthrough. Contents of this project is that proposed methods of tests for the functional regression models, functional time series model, and multivariate functional model, which are applied to practical problems. The purpose of the project is not only to enrich the theory of testing by gaining new results, but also provide the theoretical basis for the practical application and guidance.