Functional Data Correlation Test Based On Kendall Correlation Coefficient

Correlation analysis is an important part to study the relationship between two sets of data,which has important applications in various fields such as biomedicine,meteorology,engineering,etc.When analyzing and mining actual data,it is necessary to find the correlation between variables for deeper exploration such as prediction and causal analysis.Under the background of functional data,this paper mainly explores the correla-tion measurement and test of functional variables.For traditional cross section data,Kendall proposed Kendall ? correlation coefficient which measures the correlation be-tween two random variables according to the degree of synergy between them.On the functional data,the cooperative consistency of the function is defined by the maximum value and integral value of the function on the closed interval,can get measure two function variable correlation Kendall ? correlation coefficient.This paper proves that the functional data in Kendall ? correlation coefficient of asymptotic normality.It is used as a test statistic to test the correlation of functional data.Besides random function defined by the depth of the function concept of cooperative consistency,is put forward based on the functions of depth Kendall ? correlation coefficient,as a new measure of the correlation of functional variablesThe content of this paper is arranged as follows:The first chapter introduces the research background,research status of functional data correlation test.The second chapter introduces some basic knowledge about functional data.The third chapter introduces based on Kendall ? correlation coefficient of the functional data correlation test problems,and make relevant data simulation and example analysis.The fourth chapter,based on depth function is defined by the functional Kendall ? correlation coefficient,and the coefficient of simulated experiment and example analysis.The fifth chapter,conclusion and prospect.