Originally presented as the author's thesis (doctoral)--Delft University of Technology. / Includes bibliographical references (p. [185]-194) and index.

Originally presented as the author's thesis (doctoral)--Delft University of Technology. / Includes bibliographical references (p. [185]-194) and index.

Computing the least common subsumer (lcs) is an inference task that can be used to support the \bottom-up' construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts, as well as the top and the bottom concept), the lcs always exists and can efiectively be computed. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees. / An abridged version of this technical report is published in the Proceedings of IJCAI'99.

Change-point analysis is devoted to the detection and estimation of the time of structural changes within a data set of time-ordered observations. In this thesis, we estimate simultaneously multiple change-points by the least squares method and examine asymptotic properties of such estimators. Using argmin theorems, we prove weak and strong consistency under different moment conditions and investigate convergence in distribution. The identification of the limit variable allows us to derive an asymptotic confidence region for the unknown parameters. Based on a simulation study we evaluate these results.

Die generalisierte Quantilregression, einschließlich der Sonderfälle bedingter Quantile und Expektile, ist insbesondere dann eine nützliche Alternative zum bedingten Mittel bei der Charakterisierung einer bedingten Wahrscheinlichkeitsverteilung, wenn das Hauptinteresse in den Tails der Verteilung liegt. Wir bezeichnen mit v_n(x) den Kerndichteschätzer der Expektilkurve und zeigen die stark gleichmßige Konsistenzrate von v-n(x) unter allgemeinen Bedingungen. Unter Zuhilfenahme von Extremwerttheorie und starken Approximationen der empirischen Prozesse betrachten wir die asymptotischen maximalen Abweichungen sup06x61 |v_n(x) − v(x)|. Nach Vorbild der asymptotischen Theorie konstruieren wir simultane Konfidenzb änder um die geschätzte Expektilfunktion. Wir entwickeln einen funktionalen Datenanalyseansatz um eine Familie von generalisierten Quantilregressionen gemeinsam zu schätzen. Dabei gehen wir in unserem Ansatz davon aus, dass die generalisierten Quantile einige gemeinsame Merkmale teilen, welche durch eine geringe Anzahl von Hauptkomponenten zusammengefasst werden können. Die Hauptkomponenten sind als Splinefunktionen modelliert und werden durch Minimierung eines penalisierten asymmetrischen Verlustmaßes gesch¨atzt. Zur Berechnung wird ein iterativ gewichteter Kleinste-Quadrate-Algorithmus entwickelt. Während die separate Schätzung von individuell generalisierten Quantilregressionen normalerweise unter großer Variablit¨at durch fehlende Daten leidet, verbessert unser Ansatz der gemeinsamen Schätzung die Effizienz signifikant. Dies haben wir in einer Simulationsstudie demonstriert. Unsere vorgeschlagene Methode haben wir auf einen Datensatz von 150 Wetterstationen in China angewendet, um die generalisierten Quantilkurven der Volatilität der Temperatur von diesen Stationen zu erhalten / Generalized quantile regressions, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We denote $v_n(x)$ as the kernel smoothing estimator of the expectile curves. We prove the strong uniform consistency rate of $v_{n}(x)$ under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation $\sup_{ 0 \leqslant x \leqslant 1 }|v_n(x)-v(x)|$. According to the asymptotic theory, we construct simultaneous confidence bands around the estimated expectile function. We develop a functional data analysis approach to jointly estimate a family of generalized quantile regressions. Our approach assumes that the generalized quantiles share some common features that can be summarized by a small number of principal components functions. The principal components are modeled as spline functions and are estimated by minimizing a penalized asymmetric loss measure. An iteratively reweighted least squares algorithm is developed for computation. While separate estimation of individual generalized quantile regressions usually suffers from large variability due to lack of sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations