Journal of Multivariate Analysis
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Editorial: Statistics for Functional Data
Computational Statistics & Data Analysis
An overview to modelling functional data
Computational Statistics
Curve prediction and clustering with mixtures of Gaussian process functional regression models
Statistics and Computing
Estimation of a change-point in the mean function of functional data
Journal of Multivariate Analysis
Editorial: High-dimensional data: a fascinating statistical challenge
Journal of Multivariate Analysis
Testing the stability of the functional autoregressive process
Journal of Multivariate Analysis
Functional classification in Hilbert spaces
IEEE Transactions on Information Theory
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Based on the Karhunen-Loeve expansion, the maximum likelihood ratio test for the stability of sequence of Gaussian random processes is investigated. The likelihood function is based on the first p scores of eigenfunctions in the Karhunen-Loeve expansion for Gaussian random processes. Though the scores are unobservable, we show that the effect of the difference between scores and their estimators is negligible as the sample size tends to infinity. The asymptotic distribution is proved to be the Gumbel extreme value distribution. Under the alternative the test is shown to be consistent. For different choices of p, simulation results show that the test behaves quite well in finite samples. The test procedure is also applied to the annual temperature data of central England. The results show that the temperatures have risen in the last twenty years, however there is no evidence to show that the autocovariance functions of the temperatures have changed among the range of the observations.