Kumulation von Mikrodaten – Konzeptionelle Grundlagen und ein Vorschlag zur Realisierung

Zusammenfassung: In dieser Studie wird ein Konzept zur Kumulation von laufenden Haushaltsbudgetbefragungen im Rahmen des Projektes Amtliche Statistik und sozioökonomische Fragestellungen entwickelt und zur Diskussion gestellt. Dafür werden die theoretischen Grundlagen und Bausteine gelegt und die zentrale Aufgabe einer strukturellen demographischen Gewichtung mit einem Hochrechnungs–/Kalibrierungsansatz auf informationstheoretischer Basis gelöst.Vor dem Hintergrund der Wirtschaftsrechnungen des Statistischen Bundesamtes (Lfd. Wirtschaftsrechnungen und EVS) wird darauf aufbauend ein konkretes Konzept für die Kumulation von jährlichen Haushaltsbudgetbefragungen vorgeschlagen. Damit kann das Ziel einer Kumulation von Querschnitten mit einer umfassenderen Kumulationsstichprobe für tief gegliederte Analysen erreicht werden. Folgen sollen die Simulationsrechnungen zur Evaluation des Konzepts.

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Summary: In this study a concept for cumulating periodic household surveys within the frame of the project Official Statistics and Socio–Economic Questions is developed and asks for discussion. We develop the theoretical background and solve the central task of a structural demographic weighting/calibration based on an information theoretical approach.Based on the household budget surveys of the Federal Statistical Office (Periodic Household Budget Surveys and Income and Consumption Sample (EVS)) a practical concept is proposed to cumulate yearly household surveys. This allows a cumulation of cross–sections by a comprehensive cumulated sample for deeply structured analyses. In a following study this concept shall be evaluated.

     

A note on Läuter-type robust design for polynomial regression models

In this paper, we consider the problem of model robust design for simultaneous parameter estimation among a class of polynomial regression models with degree up to k. A generalized D-optimality criterion, the Ψ_α‐optimality criterion, first introduced by Läuter (1974) is considered for this problem. By applying the theory of canonical moments and the technique of maximin principle, we derive a model robust optimal design in the sense of having highest minimum Ψ_α‐efficiency. Numerical comparison indicates that the proposed design has remarkable performance for parameter estimation in all of the considered rival models.     

Detection of structural breaks in a time-varying heteroskedastic regression model

A Bayesian method for estimating a time-varying regression model subject to the presence of structural breaks is proposed. Heteroskedastic dynamics, via both GARCH and stochastic volatility specifications, and an autoregressive factor, subject to breaks, are added to generalize the standard return prediction model, in order to efficiently estimate and examine the relationship and how it changes over time. A Bayesian computational method is employed to identify the locations of structural breaks, and for estimation and inference, simultaneously accounting for heteroskedasticity and autocorrelation. The proposed methods are illustrated using simulated data. Then, an empirical study of the Taiwan and Hong Kong stock markets, using oil and gas price returns as a state variable, provides strong support for oil prices being an important explanatory variable for stock returns.     

Bayesian parametric accelerated failure time spatial model and its application to prostate cancer

Prostate cancer (PrCA) is the most common cancer diagnosed in American men and the second leading cause of death from malignancies. There are large geographical variation and racial disparities existing in the survival rate of PrCA. Much work on the spatial survival model is based on the proportional hazards (PH) model, but few focused on the accelerated failure time (AFT) model. In this paper, we investigate the PrCA data of Louisiana from the Surveillance, Epidemiology, and End Results program and the violation of the PH assumption suggests that the spatial survival model based on the AFT model is more appropriate for this data set. To account for the possible extra-variation, we consider spatially referenced independent or dependent spatial structures. The deviance information criterion is used to select a best-fitting model within the Bayesian frame work. The results from our study indicate that age, race, stage, and geographical distribution are significant in evaluating PrCA survival.     

An efficient and fast algorithm for estimating the parameters of two-dimensional sinusoidal signals

In this paper we propose a computationally efficient algorithm to estimate the parameters of a 2-D sinusoidal model in the presence of stationary noise. The estimators obtained by the proposed algorithm are consistent and asymptotically equivalent to the least squares estimators. Monte Carlo simulations are performed for different sample sizes and it is observed that the performances of the proposed method are quite satisfactory and they are equivalent to the least squares estimators. The main advantage of the proposed method is that the estimators can be obtained using only finite number of iterations. In fact it is shown that starting from the average of periodogram estimators, the proposed algorithm converges in three steps only. One synthesized texture data and one original texture data have been analyzed using the proposed algorithm for illustrative purpose.     

Geometric sample size determination in Bayesian analysis

The problem of sample size determination in the context of Bayesian analysis is considered. For the familiar and practically important parameter of a geometric distribution with a beta prior, three different Bayesian approaches based on the highest posterior density intervals are discussed. A computer program handles all computational complexities and is available upon request.     

Nonlinear regression modeling via the lasso-type regularization

We consider the problem of constructing nonlinear regression models with Gaussian basis functions, using lasso regularization. Regularization with a lasso penalty is an advantageous in that it estimates some coefficients in linear regression models to be exactly zero. We propose imposing a weighted lasso penalty on a nonlinear regression model and thereby selecting the number of basis functions effectively. In order to select tuning parameters in the regularization method, we use a deviance information criterion proposed by Spiegelhalter et al. (2002), calculating the effective number of parameters by Gibbs sampling. Simulation results demonstrate that our methodology performs well in various situations.     

On Loss Distributions from Installment-Repaid Loans

The banks have been accumulating huge data bases for many years and are increasingly turning to statistics to provide insight into customer behaviour, among other things. Credit risk is an important issue and certain stochastic models have been developed in recent years to describe and predict loan default. Two of the major models currently used in the industry are considered here, and various ways of extending their application to the case where a loan is repaid in installments are explored. The aspect of interest is the probability distribution of the total loss due to repayment default at some time. Thus, the loss distribution is determined by the distribution of times to default, here regarded as a discrete-time survival distribution. In particular, the probabilities of large losses are to be assessed for insurance purposes.     

Bayesian model selection for join point regression with application to age-adjusted cancer rates

Summary.  The method of Bayesian model selection for join point regression models is developed. Given a set of K +1 join point models M ₀,  M ₁, …,  M _K with 0, 1, …,  K join points respec-tively, the posterior distributions of the parameters and competing models M _k are computed by Markov chain Monte Carlo simulations. The Bayes information criterion BIC is used to select the model M _k with the smallest value of BIC as the best model. Another approach based on the Bayes factor selects the model M _k with the largest posterior probability as the best model when the prior distribution of M _k is discrete uniform. Both methods are applied to analyse the observed US cancer incidence rates for some selected cancer sites. The graphs of the join point models fitted to the data are produced by using the methods proposed and compared with the method of Kim and co-workers that is based on a series of permutation tests. The analyses show that the Bayes factor is sensitive to the prior specification of the variance σ ², and that the model which is selected by BIC fits the data as well as the model that is selected by the permutation test and has the advantage of producing the posterior distribution for the join points. The Bayesian join point model and model selection method that are presented here will be integrated in the National Cancer Institute's join point software ( http://www.srab.cancer.gov/joinpoint/ ) and will be available to the public.