||In this thesis, we compare two processes of detecting multiple changes in mean of functional data. Based on different alternative hypotheses, such as the AMOC alternative or the epidemic alternative, different hypothesis tests had been developed. We construct the detecting process based on the AMOC alternative. Imagine that there is a window which only contains a segment of the whole data. Different size or different location of the window makes the window contains different segment of the whole data. By changing the size or shift the location of the window, a sequence of segment data were tested for changes in mean. After the tests, we will have a result of the changes in mean of the whole data. This method is called the moving-window method. We compare it with the binary search by simulation. Ideally, the binary search could find all the changes quickly, but the simulation show a bad result. On the other hand, the moving-window method shows a better result but takes more time.|
||Aston, J. A. D. and Kirch, C. (2012) Detecting and estimating changes in dependent functional data. Journal of Multivariate Analysis 109, 204–220.|
Aue, A., Gabrys, R., Horváth, L. and Kokoszka, P. (2009) Estimation of a change-point in the mean function of functional data. Journal of Multivariate Analysis 100, 2254–2269.
Berkes, I., Gabrys, R., Horváth, L. and Kokoszka, P. (2009) Detecting changes in the mean of functional observations. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 927–946.
Hormann, S. and Kokoszka, P. (2010) Weakly dependent functional data. The Annals of Statistics Vol. 38, No. 3, 1845-1884.
Yao, F., Müller, H.-G. and Wang, J.-L. (2005) Functional Data Analysis for Sparse Longitudinal Data. Journal of the American Statistical Association Vol. 100, No. 470, 577-590.
Ramsay, J. O. and Silverman, B. W. (2005) Functional Data Analysis. New York: Springer.