Panel data analysis has become an important tool in applied econometrics and the respective statistical techniques are well described in several recent textbooks. However, for an analyst using these methods there remains the task of choosing a reasonable model for the behavior of the panel data. Of special importance is the choice between so-called fixed and random coefficient models. This choice can have a crucial effect on the interpretation of the analyzed phenomenon, which is demonstrated by an application on research and development spillover. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This dissertation proposes an iterative confidence passing (ICP) approach for parameter estimation. The dissertation describes three different algorithms that follow from this ICP approach. These three variations of the ICP approach are applied to (a) macrodiversity and user cooperation diversity reception problems, (b) the co-operative multipoint MIMO reception problem (pertinent to the LTE Advanced system scenarios), and (c) the satellite beamforming problem. The first two of these three applications are some of the significant open DSP research problems that are currently being actively pursued in academia and industry. This dissertation demonstrates a significant performance improvement that the proposed ICP approach delivers compared to the existing known techniques. The proposed ICP approach jointly estimates (and, thereby, separates) two sets of unknown parameters from the receiver measurements. For applications (a) and (b) mentioned above, one set of unknowns is comprised of the discrete-valued information-bearing transmitted symbols in a multi-channel communication system, and the other set of unknown parameters is formed by the coefficients of a Rayleigh or Rician fading channel. Application (a) is for interference-free, cooperative or macro, transmit or receive, diversity scenarios. Application (b) is for MIMO systems with interference-rich reception. Finally, application (c) is for an interference-free spacecraft array calibration system model in which both the sets of unknowns are complex continuous valued variables whose magnitude follows the Rician distribution. The algorithm described here is the outcome of an investigation for solving a difficult channel estimation problem. The difficulty of the estimation problem arises because (i) the channel of interest is intermittently observed, and (ii) the partially observed information is not directly of the channel of interest; it has dependency on another unknown and uncorrelated set of complex-valued random variables. The proposed ICP algorithmic approach for solving the above estimation problems is based on an iterative application of the Weighted Least Squares (WLS) method. The main novelty of the proposed algorithm is a back and forth exchange of the confidence or the belief values in the WLS estimates of the unknown parameters during the algorithm iterations. The confidence values of the previously obtained estimates are used to derive the estimation weights at the next iteration, which generates an improved estimate with a greater confidence. This method of iterative confidence (or belief) passing causes a bootstrapping convergence to the parameter estimates. Besides the ICP approach, several alternatives are considered to solve the above problems (a, b and c). Results of the performance simulation of the alternative methods show that the ICP algorithm outperforms all the other candidate approaches. Performance benefit is significant when the measurements (and the initial seed estimates) have non-uniform quality, e.g., when many of the measurements are either non-usable (e.g., due to shadowing or blockage) or are missing (e.g., due to instrument failures). / Ph. D.

No description available.

Diese Dissertation ist ein Beitrag zum Forschungsfeld Early stopping im Kontext iterativer Schätzverfahren. Wir betrachten Early stopping dabei sowohl aus der Perspektive impliziter Regularisierungsverfahren als auch aus der Perspektive adaptiver Methoden Analog zu expliziter Regularisierung reduziert das Stoppen eines Schätzverfahrens den stochastischen Fehler/die Varianz des endgültigen Schätzers auf Kosten eines zusätzlichen Approximationsfehlers/Bias. In diesem Forschungsbereich präsentieren wir eine neue Analyse des Gradientenabstiegsverfahrens für konvexe Lernprobleme in einem abstrakten Hilbert-Raum. Aus der Perspektive adaptiver Methoden müssen iterative Schätzerverfahren immer mit einer datengetriebenen letzten Iteration m kombiniert werden, die sowohl under- als auch over-fitting verhindert. In diesem Forschungsbereichpräsentieren wir zwei Beiträge: In einem statistischen inversen Problem, das durch iteratives Trunkieren der Singulärwertzerlegung regularisiert wird, untersuchen wir, unter welchen Umständen optimale Adaptiertheit erreicht werden kann, wenn wir an der ersten Iteration m stoppen, an der die geglätteten Residuen kleiner sind als ein kritischer Wert. Für L2-Boosting mittels Orthogonal Matching Pursuit (OMP) in hochdimensionalen linearen Modellen beweisen wir, dass sequenzielle Stoppverfahren statistische Optimalität garantieren können. Die Beweise beinhalten eine subtile punktweise Analyse einer stochastischen Bias-Varianz-Zerlegung, die durch den Greedy-Algorithmus, der OMP unterliegt, induziert wird. Simulationsstudien zeigen, dass sequentielle Methoden zu deutlich reduzierten Rechenkosten die Leistung von Standardalgorithmen wie dem kreuzvalidierten Lasso oder der nicht-sequentiellen Modellwahl über ein hochdimensionales Akaike- Kriterium erbringen können. / This dissertation contributes to the growing literature on early stopping in modern statistics and machine learning. We consider early stopping from the perspective of both implicit regularization and adaptive estimation. From the former, analogous to an explicit regularization method, halting an iterative estimation procedure reduces the stochastic error/variance of the final estimator at the cost of some bias. In this area, we present a novel analysis of gradient descent learning for convex loss functions in an abstract Hilbert space setting, which combines techniques from inexact optimization and concentration of measure. From the perspective of adaptive estimation, iterative estimation procedures have to be combined with a data-driven choice m of the effectively selected iteration in order to avoid under- as well as over-fitting. In this area, we present two contributions: For truncated SVD estimation in statistical inverse problems, we examine under what circumstances optimal adaptation can be achieved by early stopping at the first iteration at which the smoothed residuals are smaller than a critical value. For L2-boosting via orthogonal matching pursuit (OMP) in high dimensional linear models, we prove that sequential early stopping rules can preserve statistical optimality in terms of a general oracle inequality for the empirical risk and recently established optimal convergence rates for the population risk.