Covariance Function Test Of Partially Observed Functional Data

Functional data widely exist in medical,economic,meteorological and other research fields,so the statistical analysis methods of functional data have great application value.The basic idea of the functiongal data analysis is to treat the observed function as a single entity,not just as a single observation sequence.It is an important problem to test whether the covariances of functional variables are equal.Previous articles have proposed a test method based on the L2-norm,which is good when the correlation of functional data is small and there is no local spikes,but the above situation may not be satisfied in practical application.In order to solve this problem,this thesis uses the test based on the supremum-norm.Partially observed functional variables are often faced in the practical situations,which are different from the traditional method of assuming that the functional data samples are observed in the common interval.Here,it is assumed that the samples are only observed in a subset of the total interval,and the rest are missing.This problem has great application value,but the research in related fields needs to be developed.In the second chapter,we introduce the basic knowledge of test,we give the model of partial observation function data,and give the consistency estimates of covariance operator and mean function in chapter 3.Then we give the test statistic for null hypothesis of homogeneity based on supremum-norm,and study its asymptotic distribution.The theoretical distribution is very inconvenient in practical application,so we proposes to use the bootstrap method to study practical problems in chapter 4,and gives the theoretical basis of the method.Finally,the effectiveness of the proposed method is verified by numerical simulation in chapter 5.