Bayesian Semiparametric Multivariate Density Deconvolution

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls

Measurement Error in Exposure Assessment: An Error Model and its Impact on Studies on Lung Cancer and Residential Radon Exposure in Germany

Case-control studies on lung cancer and residential radon exposure had been conducted in Germany. Relative risk estimates from primary analysis were now subject to accounting for uncertainties in radon exposure and in the most potent confounder smoking. The regression calibration method and an approximate maximum likelihood method were applied. The differentiation between classical error (from assessing radon exposure or packyears) or Berkson error (from using radon exposure instead of alpha dose, from using packyears instead of inhaled dose of smoking carcinogens) was of major importance in this analysis. Estimates of relative lung cancer risk due to radon exposure were found to be higher after accounting for multiplicative classical error in radon exposure and packyears. Outliers in the data strongly influence risk estimates, but their impact is reduced, if classical error is accounted for. In one study, the influence of one outlier explained the particularly large risk-increasing impact of error correction. But also residual confounding due to adjusting for imprecisely measured packyears deflated the risk estimate in this study. It is interesting that the small correlation between radon exposure and packyears had this notable effect. On the other hand, classical errors in packyears had no large impact in the radon-prone study areas. Further, Berkson error did not induce substantial bias on the radon risk estimates, but possibly decreased the power to detect existing effects and inflated the confidence intervals. It was concluded that such an analysis was extremely valuable to understand the impact of uncertainties in the risk factor of primary interest on the risk estimate under study and the potential for residual confounding by assessment errors in the smoking variable. Note that assuming some error in the risk factors is more realistic than assuming no error. With regard to study design, study regions with no correlation between the variable of primary interest and potential confounders are preferable. However, the exact magnitude of the error could not be estimated based on the available data. Further investigations regarding residual confounding due to model mis-specification and latent smoking-related variables are necessary to grasp the full dimension of an important issue in epidemiology, i.e. the role of the outstanding confounder smoking for estimating small risks.In Deutschland waren Fall-Kontroll-Studien zu Lungenkrebs und Radon in Innenräumen durchgeführt worden. In der Schätzung des relativen Lungenkrebsrisikos wurden nun Unsicherheiten in der Radonexposition und im stärksten potentiellen „Confounder" Rauchen berücksichtigt. Hierbei wurden die Methode der Regressionscalibrierung und eine approximative „Maximum Likelihood" Methode angewandt. Die Unterscheidung zwischen klassischem Fehler (durch Erhebung der Radonexposition oder der Packungsjahre) und Berkson-Fehler (durch Verwendung von Radonexposition als Surrogat für Alpha-Dosis oder von Packungsjahren als Surrogat für Lungendosis durch inhalierte Karzinogene im Rauch) war von besonderer Bedeutung in dieser Analyse. Die Risikoschätzer waren höher, wenn multiplikative klassische Messfehler in der Erhebung der Radonexposition und der Packungsjahre berücksichtigt wurden. Ausreißer in den Daten haben einen starken Einfluß auf Risikoschätzer, welcher jedoch durch Berücksichtigung klassischer Fehler reduziert wird. In einer Studie erklärte der Einfluß eines Ausreißers den besonders starken das Risiko erhöhenden Effekt der Fehlerkorrektur. Aber auch „Residual Confounding" durch Adjustierung für ungenau erhobene Packungsjahre verringerte das beobachtete Risiko in dieser Studie. Es ist interessant, dass sich die kleine Korrelation zwischen Radonexposition und den Packungsjahren so stark auswirkte. In höher mit Radon belasteten Studiengebieten hatten klassische Fehler in den Packungsjahren keinen großen Effekt. Ferner bewirkte der Berkson-Fehler keine nennenswerte Verzerrung der Risikoschätzer, aber schmälerte die „Power", um existierende Effekte zu erkennen. Diese Analyse war extrem nützlich, um die Auswirkung von Messfehlern im primären Risikofaktor auf das zu untersuchende Risiko und das Potential von „Residual Confounding" durch Fehler in der Rauchvariablen zu verstehen. Man halte sich vor Augen, dass die Annahme irgendeines Fehlers in den Risikofaktoren realistischer ist als die Annahme keines Fehlers. Bezüglich des Studiendesigns, ist eine Studienregion, wo die Primärexposition nicht mit dem potentiellen „Confounder" korreliert ist, vorzuziehen. Die genaue Fehlergröße konnte jedoch nicht aus den zur Verfügung stehenden Daten geschätzt werden. Außerdem sind weitere Untersuchungen hinsichtlich des „Residual Confounding" durch Modell-Fehlspezifikation und latente Rauchvariable notwendig, um das volle Ausmaß eines wichtigen Punktes in der Epidemiologie zu verstehen, nämlich die Rolle des herausragenden „Confounder" Rauchen für die Schätzung kleiner Risiken

Three Essays on Volatility Forecasting and Forecast Evaluation

The three main chapters of this dissertation are self-contained research articles that can be read independently from each other. They all focus on forecasting with financial and macroeconomic data. The analyses in Chapter 1 and 2 are joint works with Christian Conrad. Both focus on forecasting volatility for financial markets. In Chapter 1, we address aggregate stock market volatility and in Chapter 2 stock-specific volatility for investment decisions. Chapter 3 is single-authored and, in contrast to the other two chapters, focuses on the evaluation of distribution forecasts

A state space model for exponential smoothing with group seasonality

We present an approach to improve forecast accuracy by simultaneously forecasting a group of products that exhibit similar seasonal demand patterns. Better seasonality estimates can be made by using information on all products in a group, and using these improved estimates when forecasting at the individual product level. This approach is called the group seasonal indices (GSI) approach, and is a generalization of the classical Holt-Winters procedure. This article describes an underlying state space model for this method and presents simulation results that show when it yields more accurate forecasts than Holt-Winters.Common seasonality; demand forecasting; exponential smoothing; Holt-Winters; state space model.