| Abstract [eng] |
This dissertation develops nonparametric procedures for detecting changed segments (epidemic-type change-points) in function-valued samples: the data-generating distribution is tested for homogeneity against an alternative under which observations on an unknown contiguous interval are drawn from a different distribution. Three complementary families of scan statistics are constructed: Wilcoxon-type tests built from antisymmetric kernels; Lp-type (Cramér–von Mises) statistics that aggregate empirical-process increments; and RKHS-distance tests based on kernel mean embeddings. All three families act on scalar features obtained via Brownian (Itô), L2-norm, and C-type max-variance projections of the functional sample. For each family, null limit distributions are derived as functionals of Brownian bridge and Wiener sheet Gaussian processes, with an admissible weight class controlling the trade-off between sensitivity to short and long segments. Monte Carlo experiments calibrate size and compare power across diverse alternatives. The three families prove complementary, each strongest for a different structure of change. The methodology is demonstrated on Lithuanian electricity balancing prices, where it identifies interpretable epidemic-type departures robust to preprocessing choices. |
