Dienstag, 5. Mai 2009, 11-12 Uhr - Raum: W9-109
Functional linear regression
Prof. Dr. Alois Kneip
Universität Bonn
The talk considers functional linear regression, where scalar responses are modeled in dependence of random functions. Different types of estimators are proposed and the focus lies upon spline estimators for the functional slope parameter. Connections to the literature on sparse, high-dimensional regression problems are elaborated. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. It is then proved that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predictive curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day.
Dienstag, 19. Mai 2009, 11-12 Uhr - Raum: W9-109
Penalized Density Estimation
Dipl. Wirt.-Math. Christian Schellhase
Universität Bielefeld
Estimation of an unknown density is of much interest in many fields of research. The link between penalized spline estimation and mixed models will be in focus of this approach of penalized density estimation. The idea is to approximate the unknown density by a linear combination of a large number of fixed mixture densities, while the weights are fitted with penalized techniques to obtain a smooth density fit. It is of interest to extend the classical density estimation problem by directly allowing the density to depend on some covariates, restricted to factorial quantities. The usefulness of this idea is illustrated at simulations studies using the corresponding R-package pendensity. These simulations show satisfactory results of the proposal of penalized density estimation. Compared to known density estimation approaches from Eilers and Marx (1996) or from Wand and Jones (1995), the penalized density estimation shows a better or approximately equal mean squared error of the fitted densities in several simulation studies.
Duration of maternity leave in Germany
Dipl.-Kfm. Dipl.-Volksw. Torben Kuhlenkasper
Universität Bielefeld
The talk presents an investigation of maternity leave behavior in West Germany for females being employed between 1995 and 2006 using data from the German Socio Economic Panel. The observational study focuses on the investigation of individual and family-related covariate effects on the duration of maternity leave following first or second childbirth, respectively. Dynamic duration time models are used in which covariate effects are allowed to vary smoothly with duration of not being in the job after bearing a child. The intention of the paper is to demonstrate with state of the art models how effects of covariables change over time and to analyse substantial differences between maternity leaves following first and second childbirth. Particularly the personal income of mothers before their first maternity leave and the educational attainment influence the decision when to return into employment. The leave period following second birth is influenced by the mothers' attachment to the labour market between their two maternity leave periods. As fitting routine penalized spline smoothing effects is employed using available software in R (www.r-project.org).
Dienstag, 2. Juni 2009, 11:30-12 Uhr - Raum: W9-109
Modellierung diskreter Auswahlprozesse unter Berücksichtigung von nicht-kompensatorischen Entscheidungsheuristiken
Dipl.-Kfm. Sören Scholz
Universität Bielefeld
Dienstag, 16. Juni 2009, 11-12 Uhr - Raum: W9-109
Assessing Parametric Misspecification and Heterogeneity in Growth Regressions
Dipl.-Vw. Verena Petring
Universität Bielefeld
A fully non-parametric analysis is applied to address the problems of nonlinearity and heterogeneity in classical growth regression models using original data from seminal contributions in this field. Non-parametric specification tests and in-sample goodness-of-fit measures, as well as cross-validation based out-of sample measures provide considerable evidence for parametric misspecification and a superior performance of a nonparametric model, despite the small sample size. In contrast to recent contributions identifying heterogeneity as the primal source of misspecification, a formal and graphical analysis does not reveal evidence for heterogeneity in a parametric and non-parametric quantile regression framework.
Latent Transition Analysis: Testing the gateway theory of drug involvement
Luca Mariotti
Universität Bielefeld
There is a general consensus in the public debate that the assumption of drugs follows a specific path: from legal to illegal, from "soft" to "harder" drugs. This idea has been empirically proved by Kandel (1975), and summarized thereafter in the so called gateway theory of drug involvement. Further studies conducted by Collin and colleagues (see Collins & Wugalter, 1992) by means of latent transition analysis (LTA) confirmed that the sequence of drug consumption involves first the use of tobacco and/or alcohol, then moves tolight illegal drugs such as marijuana, and only after includes the consumption of more dangerous drugs. The sequence within this last category is, however, not yet clear. In this work the pathways of drug use among adolescents will be analysed by means of a mover/stayer model (Pol & Langeheine, 1989) - which is a special case of latent transition analysis -, using the first five waves of the longitudinastudy Crime in the modern city (CriMoC), which has been carried out for the last eight years in the German town of Duisburg. The results confirm that in middle adolescence young users tend to follow a specific path in the choice of which drug to use, starting with alcohol and ending with hard drugs.
Dienstag, 23.Juni 2009, 11-12 Uhr - Raum: W9-109
Second-order stochastic differential equation model as an alternative for the ALT and CALT models
Prof. Dr. Han Oud
Radboud University Nijmegen
In the structural equation modeling (SEM) literature, two models for the analysis of longitudinal data became very popular in the past: autoregressive (AR) cross-lagged models and latent trajectory (LT) models. Curran and Bollen (2001) and Bollen and Curran (2004), however, argued that, theoretically, there are many instances when both the processes described by the AR model and the processes described by the LT model are plausible. They proposed the autoregressive latent trajectory (ALT) model, which captures features of both. The discrete-time approach in the ALT model has been criticized by Delsing and Oud (2008), who proposed a continuous time version of the ALT model, using stochastic differential equations, called “continuous time autoregressive latent trajectory” (CALT) model. In the paper, the linear component appearing in both the ALT and the CALT models will be criticized on several counts. It is shown that most of the problems associated with the linear component are solved by a second-order stochastic differential equation model.
Dienstag, 14. Juli 2009, 11-12 Uhr - Raum: W9-109
Semiparametric modelling of different volatility components in high-frequency financial time series
Prof. Dr. Yuanhua Feng
Universität Paderborn
This paper extends the GARCH model to a wide class of nonstationary processes by proposing a semiparametric GARCH model for simultaneous modelling of conditional heteroskedasticity, slow scale change and periodicity in the volatility of highfrequency financial returns. A data-driven algorithm is developed for estimating the model. An approximate significance test of daily periodicity and the use of Monte Carlo confidence bounds for the scale function are proposed. The practical performance of the proposal is investigated in detail using some German stock price returns. It is shown that the various volatility components are all significant. Asymptotic properties of the proposed estimators are investigated.