Modified cross-validation in density estimation

We propose a new modified (biased) cross-validation method for adaptively determining the bandwidth in a nonparametric density estimation setup. It is shown that the method provides consistent minimizers. Some simulation results are reported on which compare the small sample behavior of the new and the classical cross-validation selectors.     

The Jackknife estimate of covariance of two Kaplan–Meier integrals with covariables

In this paper the Jackknife estimate of covariance of two Kaplan–Meier integrals with covariates is introduced. Its strong consistency is established under mild conditions. Several applications of the estimator are discussed.     

Preis-Promotion-Framing – Ein Überblick zum Stand der Forschung

This article reviews published literature and provides an overview on present empirical evidence about the framing of price promotions. Concerning explicit price reductions (discounts, coupons, rebates), the effects of advertised reference prices and different frames of price discounts (relative versus absolute price discount, objective versus tensile price claims) on consumers’ reactions are discussed. Furthermore, the article examines empirical results on implicit price reductions (volume packs, free extra products) as well as on sale signs and restrictions (e.g. purchase limits, time limits) as popular ways of framing a deal. The key findings point out that framing a price promotion in different ways can affect consumers’ perceptions and evaluations of the deal. Based on the reviewed literature, the concluding section provides managerial implications and an agenda for further research.     

Kernel adjusted nonparametric regression

In this paper we propose and study a new kernel regression estimator in which the kernel is taken from a properly adapted location-scale family of the design distribution. We show that, while the original smoothing may be performed with sub-optimal bandwidths, adaptation of proper scale parameters yields overall optimal estimators. Unlike traditional smoothing methodology, our approach does not aim at estimating pivotal higher order derivatives.     

Zur verknüpfung von “zeitbereichsanlalyse” und “frequenzbereichsanalyse” bei saisonbereinigungsverfahren-ein beitrag zur zeitreihenanaiyse

It is charaateristic feature of the serasonal adjusment procedures generally used today that their theoretical basis consists of analyses both in the time – and frequency – domain. However, both methods of analysis are unconnected hitherto. In addition, even the modern statistical concepts considering the transfer functions of the filters used, show definitorial deficiencies, since the lengths of the lengths of the relevant frequency bands are not determined objectively. Therefore in the following paper the problems of a possible connection of both methods of analysis and a solution of the aforementioned definitorial problems by using concepts of statistical estimation theory is analyzed.     

The statistical impact of inflation on interest rates

Understanding the behavior of interest rates is of central importance in finance. This is due to the fact that interest and forward rates serve as underlyings for many fixed income products. Furthermore, interest rate-based quantities may be used as numeraires when it comes to computing present values of future payoffs. An important macroeconomic factor which is likely to trigger interest rates is inflation. In this paper we extend a well-known continuous time interest rate model by incorporating inflation. Finally, we apply a statistical test to real data to explore the goodness-of-fit of the inflation-based model.     

Improved estimation under random censorship

In this article we propose a variant of the Kaplan-Meier estimator which aims at reducing the bias by adding a bootstrap based correction term to the pertaining cumulative hazard function. For the mean lifetime it is demonstrated in a simulation study that the new estimator also has a smaller variance.     

Zur Berücksichtigung von Heterogenit?t versus funktionaler Flexibilit?t in Absatzreaktionsmodellen: Eine empirische Studie auf Basis von Handelsdaten

In this paper, we explore the differences between store sales models that allow for heterogeneity in marketing effects across stores and models that accommodate potential irregularities in sales response through the use of nonparametric estimation techniques. In particular, we investigate the following question: What benefits can we gain from incorporating store heterogeneity versus functional flexibility in sales response models concerning fit and predictive validity, as compared to a simple parametric store sales model? In an empirical study based on store-level data, we also compare the different model versions with respect to estimated price elasticities and resulting shapes for own- and cross-price effects. Our empirical results indicate that addressing heterogeneity is not advantageous in general, as model fit, predictive validity and the accuracy of price elasticities did not improve for many brands. In contrast, estimating sales response flexibly provides much more potential for statistical improvements and leads to different implications concerning price elasticities, too.     

Financing the statutory pensions insurance scheme in a united Germany

This article outlines the development of the predominant scheme of old-age protection in Germany (the statutory pensions insurance scheme) within the framework of the process of unifying the two post-war German states. The systems of old-age protection in West and East Germany had evolved very differently after the Second World War, so that a major transformation was needed. The various stages of bringing the schemes together are described, including the conversion of pensions in the German Democratic Republic when the Deutschmark was introduced on 1 July 1990, the raising of pensions, and the considerable further adjustments that took place later. Finally, the process of applying West German pensions legislation to East Germany is described. This legislation resulted from a Pensions Reform Act which was adopted on 9 November 1989 with the purpose of adapting the system of old-age protection to changing structural conditions affecting the composition of the population, the economy and society as a whole. The article is completed by a look at the evolution of the financial requirements for pensions insurance over the medium and long term.     

Changepoint Problems Under Random Censorship

Let X ₁, …, X _[nθ], X _{[nθ] + 1}, …, X _n be a sequence of independent random variables (the “lifetimes”) such that X _j ? F ₁ for 1 ≤ j ≤ [nθ] and X _j ? F ₂ for [nθ] + 1 ≤ j ≤ n, with F ₁ ≠ F ₂ unknown. In this paper we investigate an estimator θ _n for the changepoint θ if the X's are subject to censoring. The rate of almost sure convergence of θ _n to θ is established and a test for the hypothesis θ = 0, i.e. “no change”, is proposed.