Testing Functional Data Based On Ranks

With the continuous development of data collection technology,data types show a trend of diversification.A class of complex data represented by functional data has been widely concerned by scholars.In the field of medicine and meteorology,a large number of functional data can usually be seen,and the functional data with infinite dimensional characteristics contain rich information.This paper mainly studies the hypothesis testing of functional data.Firstly,for the two-sample mean test of functional data,this paper constructs the test statistics based on two methods of defining the curve rank,and deduces its asymptotic normality under the null hypothesis and the alternative hypothesis.This test method performs well in both numerical simulation and case analysis.Secondly,Spearman rank correlation coefficient of functional data was proposed in this paper,and the classical Spearman rank correlation coefficient was extended to functional data.As a test statistic of correlation test,its asymptotic normality is derived theoretically.A large number of simulation studies show that it can measure the correlation of bivariate functional data well and has robustness.In the part of case analysis,the correlation test was applied to the renal dialysis pressure data,and the test results were consistent with the medical knowledge.The contents of this paper are arranged as follows: the first chapter mainly introduces the research background and current situation of functional data test;The second chapter introduces the basic concepts and theorems related to the test method.In the third chapter,the two sample mean test of functional data is discussed,and the asymptotic normality of test statistics is proved.In chapter 4,Spearman rank correlation coefficient of correlation of measurement function data was constructed and used to test the correlation of binary function data.The validity of the test method was illustrated by numerical simulation and case analysis.Chapter five,conclusion and prospect.