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.     

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.     

Über asymptotisch optimale versuchsplanung im sinne von sacks-ylvisaker

Zusammenfassunf.Das Versuchplanungsproblem von Sacks-Ylvisaker in der Form von Hajek-Kimeldorf wird unter etwas veränderten voraussetzungen betrachtet.Dieses Resultat wird zur Lösung eines speziellen problems der Versuchsplanung für zufällige Felder verwendet.     

Schätzungen in Stochastischen Differenzen-und Differentialgleiehungssystemen 2

Some ways of Studentizing the parametric c-sample tests (c≧2) for location are examined and their asymptotic properties established. A way of Studentizing the c-sample Puni test based on the ranks of the observations is proposed. The resulting test is shown to be asymptotically valid and consistent for a reasonable class of alternatives     

Die waldsche fundamentalidentität und ein sequentieller quotiententest für eine zufäallige irrfahrtüber einer homogenen irreduziblen markovschen kette mit endlichem zustandsraum

For a random walk {R _n ≥0} given on a homogeneous irreducible finite MARKOV chain {X _n ≥0} the identity (8) is obtained. Generalizations (14)-(16) of WALD's Fundamental Identity and WALD's first and second equations for the two-dimensional process {(R _n ,X _n ), n≥0} are proved. The Average Sample Number (21)-(22) and the Operating Characteristic Function (24)-(25) of a Sequential Probability Ratio Test follow. With this test a decision about two simple hypotheses on the unknown transition probability matrix of {X _n , n≥0} and the unknown parameters of the probability distributions for the increments of {X _n , n≥0} can be made. For a special case these results were proved by PHATARFOD [6] and KüCHLER [3] with other methods.     

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.

     

Statistische Analyse ausgewählter Schätzer im kontemporär korrelierten Regressionsmodell mit prädeterminiertem verzögerten Regressor und autokorrelierten Fehlern

Under a weaker assumption of independency apartial analysis of single equations is possiblewithout the specification of a simultaneous equation model. In the extended simple regression model with the weaker independency assumption the OLS-estimator turns out to bequite robust, even in extreme variations, whereas the GLS-estimator shows agreat sensitivity with regard to the modification of the independency. A Monte Carlo study confirms the results concerning the asymptotic bias and indicates a higher variance for the GLS- than for the OLS-estimator. In small samples the standard deviation of the OLS-estimator is smaller than the deviation of a consistent instrumental variables estimator which asymptotic efficiency loss compared to the efficient GLS-estimator in the stochastically independent regression is small as long as the regressor has a high autocorrelation.     

Zuverlässigkeitsmodelle auf der Grundlage stochastischer Modelle von Verschleiß prozessen

Reliability of products of mechanical engineering is often decided by wear processes.

Suitable stcohastic precesses (cumulative stochastic precesses, Wiener-process with drift and related multiplicative processes) are applied to modelling of such wear processes. Then the lifetime is the random time to first crossing a given limiting wear level or wear reserve. Some lifetime distributions which are founded in such a wag for constant and random wear reserves are discussed (Birnbaum-Saunders-distribution, Inverse-Gaussian-distribution, special mixtures of distributions).

For some of these models a favourable statistical approach to lifetime distribution arises from samples of the wear process. Process. Possibilities to calculate characteristics or ordinary renewal processes are dealt with. In essential cases such characteristics can be expressed explicity.

By an example the application of the results is demonstrated beginning with samples from the wear process followed by choosing a wear model, estimating the parameters, testing goodness of fit, calculating characteristics of reliability up to optimal designing of block replacement in preventive maintenance and calculating the technical-founded demand for replacement parts.     

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.