Über das asymptotische verhalten von bayesschen und maximum-likelihood-schätzungen

The paper deals with the asymptotic equivalence of the maximum-likelihood-estimator with sums of independent and identically distributed random variables for a family of distribution functions, the density of which may vanish depending on the parameter. Further the asymptotic equivalence of the maximum-likelihood-estimator with BAYES estimators is shown.     

Über die asymptotische verteilung des periodogramms stationärer gaussscher zufälliger folgen

For stationary Gaussian random sequences it is estimated the rate of convergence to the asymptotic distribution of the periodogram. An asymptotic expansio for the distribution function of the periodogram is given as well.     

Zur bestimmung von bayes-lösungen bei messender prüfung

A model of sampling inspection by variables is presented, where the loss function and the a priori distribution of the unknown defective fraction are assumed to be known. The existence of a BAYES rule in the class of relevant decision functions (sampling plans) is proved. Furthermore, it is shown that under certain conditions the decision functions "accept without sampling" or "reject without sampling" are BAYESian decision rules. Some numerical examples are presented to illustrate the theory developed in the paper.     

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.

     

Bernstein–von Mises Theorem for M|M|1 Queue

The article deals with Bernstein–von Mises theorem, for the arrival process in a M | M |1 queue.     

On conjugate families and Jeffreys priors for von Mises–Fisher distributions

This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises–Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises–Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises–Fisher distributions on Stiefel manifolds.     

A Bayesian Analysis of Directional Data Using the von Mises–Fisher Distribution

ABSTRACT

This article presents a Bayesian analysis of the von Mises–Fisher distribution, which is the most important distribution in the analysis of directional data. We obtain samples from the posterior distribution using a sampling-importance-resampling method. The procedure is illustrated using simulated data as well as real data sets previously analyzed in the literature.     

Tables for the Lilliefors and Modified Cramer–von Mises Tests of Normality

We present new tabulations of the Lilliefors distribution and the modified Cramer–von Mises distribution, which are used to test for normality when the population mean and variance are unknown. Some practical remarks and an example are given.     

Zur abschätzung von lösungen linearer integralgleichungen mit hilfe der monte-carlo-methode

Let X₁, X₂, … be i.i.d.r.v. and write (X₁+…X_n?A_n)/B_n?F_n, where B_n >0.A_nER₁, n≥1. It is known that solely one–sided asymptotic assumptions imposed on F_n imply F_n0. In the present note we show that stronger one–sided assumptions lead even to the existence of EX₁ ³ so that the BERRY-ESSEEN inequalities hold true.     

Bewertung von sheätzungen bei einem linearen modell auf der grundlage des fiduzialkonzepts

Usingf fiducial inference the quality of estimations is investigated for a linear model under the conditionj that information about the vector to be estimated is derived from a small sample. By application of that model to the deduction of atmospheric temperature profiles the obtained results are illustrated numerically.     

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.     

On Cramér–von Mises type test based on local time of switching diffusion process

We consider a Cramér–von Mises type test for hypothesis that the observed diffusion process has sign-type trend coefficient based on empirical density function. It is shown that the limit distribution of the proposed test statistic is defined by the integral type functional of continuous Gaussian process. We provide the Karhunen–Loève expansion of the corresponding limiting process. Approximation of the threshold is given through the representation for the limit statistic.     

Zur experimeatellen Bildung dynamiseher Modelle für die automatische Steuerung von Systemen - eine übersicht 2

Es wird eine gestuerte stochastische Differenzengleichung für zufällige Felder betrachtet. Es werden ein Extremalprinzip bewiesen und die Dualität zwischen der linearen filtration zufälliger Felder und der derministischen optimalen steuerung diskutiert