TY - RPRT A1 - Nastansky, Andreas T1 - Topologische Datenanalyse BT - Eine Einführung in die Persistente Homologie und Mapper T2 - Statistische Diskussionsbeiträge N2 - Bei der Analyse von höherdimensionalen Daten kann deren Gestalt wichtige Informationen über den Datensatz liefern. Bei einer gegebenen Punktwolke, die aus einem unbekannten topologischen Raum ausgewählt wurde, versucht die Topologische Datenanalyse (TDA) den ursprünglichen Raum zu rekonstruieren. Dieser Beitrag soll eine Einführung in die Topologische Datenanalyse geben und konzentriert sich dabei auf zwei wichtige Aspekte: die Persistente Homologie und den Mapper. Dabei werden zuerst die notwendigen theoretischen Grundlagen vorgestellt und anschließend wird die Methodik bei der Visualisierung von Daten eingesetzt. Die Persistente Homologie ist eines der Standardwerkzeuge in der TDA. Sie findet ihre Anwendung beispielsweise in den Bereichen Formerkennung und -beschreibung. Der Mapper als zweites wichtiges Konzept der TDA wandelt umfangreiche, höherdimensionale Datensätze in Simplizialkomplexe um und kann dadurch geometrische und topologische Eigenschaften der Daten bestimmen. Des Weiteren ist die Mapper-Methode ein brauchbares Werkzeug zur Visualisierungen von mehrdimensionalen Daten, woran statistische Verfahren scheitern. N2 - In the analysis of higher-dimensional data their shape can provide important information about the dataset. Given a point cloud sampled from an unknown topological space, topological data analysis tries to reconstruct the original space. This paper provides an introduction into topological data analysis (TDA) and focuses on two important aspects: Persistent Homology and Mapper. First, the theoretical basics are introduced and then the methodology is applied to visualize data. Persistent Homology represents a standard tools in the TDA. This approach is used, for example, in shape recognition and description. The Mapper is a second important concept of the TDA and converts wide, higher-dimensional datasets into simplicial complexes. By that it can determine geometric and topological properties of the data. Furthermore, the Mapper method is a useful tool for the visualization of multi-dimensional data, where statistical methods fail. T3 - Statistische Diskussionsbeiträge - 53 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-431420 IS - 53 ER - TY - RPRT A1 - Müller, Kai-Uwe A1 - Wrohlich, Katharina T1 - Does subsidized care for toddlers increase maternal labor supply? BT - Evidence from a large-scale expansion of early childcare T2 - CEPA Discussion Papers N2 - Expanding public or publicly subsidized childcare has been a top social policy priority in many industrialized countries. It is supposed to increase fertility, promote children’s development and enhance mothers’ labor market attachment. In this paper, we analyze the causal effect of one of the largest expansions of subsidized childcare for children up to three years among industrialized countries on the employment of mothers in Germany. Identification is based on spatial and temporal variation in the expansion of publicly subsidized childcare triggered by two comprehensive childcare policy reforms. The empirical analysis is based on the German Microcensus that is matched to county level data on childcare availability. Based on our preferred specification which includes time and county fixed effects we find that an increase in childcare slots by one percentage point increases mothers’ labor market participation rate by 0.2 percentage points. The overall increase in employment is explained by the rise in part-time employment with relatively long hours (20-35 hours per week). We do not find a change in full-time employment or lower part-time employment that is causally related to the childcare expansion. The effect is almost entirely driven by mothers with medium-level qualifications. Mothers with low education levels do not profit from this reform calling for a stronger policy focus on particularly disadvantaged groups in coming years. T3 - CEPA Discussion Papers - 9 KW - childcare provision KW - mother’s labor supply KW - generalized difference-in-difference Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-427727 SN - 2628-653X IS - 9 ER -