|Title:||Robust change-point detection and dependence modeling|
|Abstract:||This doctoral thesis consists of three parts: robust estimation of the autocorrelation function, the spatial sign correlation, and robust change-point detection in panel data. Albeit covering quite different statistical branches like time series analysis, multivariate analysis, and change-point detection, there is a common issue in all of the sections and this is robustness. Robustness is in the sense that the statistical analysis should stay reliable if there is a small fraction of observations which do not follow the chosen model. The first part of the thesis is a review study comparing different proposals for robust estimation of the autocorrelation function. Over the years many estimators have been proposed but thorough comparisons are missing, resulting in a lack of knowledge which estimator is preferable in which situation. We treat this problem, though we mainly concentrate on a special but nonetheless very popular case where the bulk of observations is generated from a linear Gaussian process. The second chapter deals with something congeneric, namely measuring dependence through the spatial sign correlation, a robust and within the elliptic model distribution-free estimator for the correlation based on the spatial sign covariance matrix. We derive its asymptotic distribution and robustness properties like influence function and gross error sensitivity. Furthermore we propose a two stage version which improves both efficiency under normality and robustness. The surprisingly simple formula of its asymptotic variance is used to construct a variance stabilizing transformation, which enables us to calculate very accurate confidence intervals, which are distribution-free within the elliptic model. We also propose a positive semi-definite multivariate spatial sign correlation, which is more efficient but less robust than its bivariate counterpart. The third chapter deals with a robust test for a location change in panel data under serial dependence. Robustness is achieved by using robust scores, which are calculated by applying psi-functions. The main focus here is to derive asymptotics under the null hypothesis of a stationary panel, if both the number of individuals and time points tend to infinity. We can show under some regularity assumptions that the limiting distribution does not depend on the underlying distribution of the panel as long as we have short range dependence in the time dimension and ndependence in the cross sectional dimension.|
Spatial sign covariance matrix
|Subject Headings (RSWK):||Robuste Schätzung|
|Appears in Collections:||Fachgebiet Statistik in den Biowissenschaften|
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