Showing papers in "Metrika in 1979"
TL;DR: In this article, the asymptotic distribution for a certain class of functionals of distribution functions is derived, and the results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned functionals.
Abstract: The asymptotic distribution for a certain class of functionals of distribution functions is derived. This result is used to give distribution free asymptotic confidence intervals for these functionals; for this purpose, a strongly consistent estimate for the asymptotic variance is constructed. These results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned class of functionals.
39 citations
TL;DR: In this article, the authors show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terms (ARIMA-models).
Abstract: Wold's decomposition theorem [Wold] states that every weakly stationary stochastic process can be written as a linear combination of orthogonal shocks. For practical reasons, however, it is desirable to employ models which use parameters parsimoniously.Box andJenkins [1970] show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terms (ARIMA-models). The Gaussian hypothesis assumes that the shocks follow a normal distribution with fixed mean and variance. In this case the process is characterized by first and second order moments. The normality assumption seems reasonable for many kinds of series. However, it was pointed out byKendall [1953],Mandelbrot [1963, 1967],Fama [1965],Mandelbrot andTaylor [1967] that particularly for stock price data the distribution of the shocks appears leptokurtic:
11 citations
TL;DR: In this article, a nonparametric test based on extremal quotient (EQ) was proposed for testing the null hypothesis that the population of the sample has an exponential distribution against a hypothesis that it does not.
Abstract: A procedure based on the extremal quotient is proposed for testing the null hypothesis
H
0: the population of the sample has an exponential distribution against
H
a
: it does not have an exponential distribution. The proposed procedure is a nonparametric test which could lead to an early decision for the rejection ofH
0
10 citations
TL;DR: In this article, the authors give invariant optimal estimators for functions of probability densities, based on independent observations in a homogeneous space, for derivatives of the density, densities of order statistics and of empirical means.
Abstract: This note gives invariantly optimal estimators for functions of probability densities, based on independent observations in a homogeneous space. The results are applied to the estimation of certain densities, derivatives of the density, densities of order statistics and of empirical means.
9 citations
TL;DR: In this article, a characterization of the exponential law is given using its property that E[(X−a)r|X>a] is constant for alla≧0, r being a positive integer.
Abstract: A characterization of the exponential law is given using its property thatE[(X−a)r|X>a] is constant for alla≧0,r being a positive integer. Then this result is applied to the order statistics and some further characterizations are found.
9 citations
Journal Article•
6 citations
TL;DR: In this article, a sequential stochastic process is observed in discrete time intervals; the process is generated by Bernoulli trials with unknown mean p, and given an a-priori distribution forp, regarded as a random variable, and discounting future payoffs with a factor ν, O<ν<1, optimal and suboptimal stopping rules (depending on ν) are constructed.
Abstract: A sequential stochastic process is observed in discrete time intervals; the process is generated by Bernoulli trials with unknown meanp. Given an a-priori distribution forp, regarded as a random variable, and discounting future payoffs with a factor ν, O<ν<1, optimal and suboptimal stopping rules (depending on ν) are constructed. this leads to the connection of the process under consideration with another process of the same structure, but with known meanPo for the Bernoulli trials, thus finally resulting in an One-Armed-Bandit problem.
5 citations
TL;DR: In this paper, a nonparametric test is proposed for testing differences of location in two independent samples without assuming equal scale parameters of the respective populations, based on simultaneous application of two modified median tests.
Abstract: A non-parametric test is proposed for testing differences of location in two independent samples without assuming equal scale parameters of the respective populations. The test is based on simultaneous application of two modified median tests, each using its sample median of the single samples.
4 citations
TL;DR: In this paper, the estimation of the regression coefficient of a population, defined byE (y)= γ+βx, incorporating two preliminary tests of significance has been discussed, where the experimenter has two random samples of different sizes from two such populations, as defined above, with regression coefficientsβ1 andβ2 respectively, whereβ2 may possibly be equal to β1.
Abstract: The estimation of the regression coefficient of a population, defined byE (y)= γ+βx, incorporating two preliminary tests of significance has been discussed. The experimenter has two random samples of different sizes from two such populations, as defined above, with regression coefficientsβ1 andβ2 respectively, whereβ2 may possibly be equal toβ1. Besides this, it is also conjectured that the common conditional varianceσ2 of the two populations has a specified valueσ 0 2 . The two preliminary tests are used to resolve these two uncertainties.
4 citations
TL;DR: In this article, a Verallgemeinerung of nichtzentralent-Testes zum Prufen von Ausschusanteilen darstellt.
Abstract: Es wird ein Test angegeben, der eine Verallgemeinerung des nichtzentralent-Testes zum Prufen von Ausschusanteilen darstellt. Die Verallgemeinerung betrifft die Voraussetzung der Normalverteilung. Die asymptotischen Eigenschaften fur grose Stichproben werden hergeleitet. Dabei zeigt sich u.a., in welcher Weise die Anwendung des klassischen nichtzentralent-Testes zu Fehlschlussen fuhrt, wenn keine Normalverteilung vorliegt.
3 citations
TL;DR: In this article, die asymptotische Verteilung von Maximum Probability Schatzern unter Voraussetzung der asymPTotischen Normalitat der Loglikelihoodquotienten gezeigt.
Abstract: Unter allgemeinen Voraussetzungen uber den Likelihoodquotienten wird die Konsistenz des Maximum Probability Schatzers gezeigt. Ferner wird die asymptotische Verteilung von Maximum Probability Schatzern unter Voraussetzung der asymptotischen Normalitat der Loglikelihoodquotienten gezeigt.
TL;DR: In this article, the authors extend their analysis to cover the case of several latent variables and use a maximum likelihood procedure to estimate the parameters of a model in which one observes multiple indicators and multiple causes of a single latent variable.
Abstract: Joreskog/Goldberger [1975] use a maximum likelihood procedure to estimate the parameters of a model in which one observes multiple indicators and multiple causes of a single latent variable. This note extends their analysis to cover the case of several latent variables.
TL;DR: The multivariate normal distribution is characterized in the class of infinitely divisible distributions.
Abstract: The multivariate normal distribution is characterized in the class of infinitely divisible distributions.
TL;DR: In this paper, the Robbins-Monroe Prozes with stetigem Parameter studiert is studied, and a new Methode (Vergleich with expliziten Losungen) is introduced.
Abstract: In dieser Arbeit wird der Robbins-Monroe Prozes mit stetigem Parameter studiert. Durch eine neue Methode (Vergleich mit expliziten Losungen) konnen verschiedene Aspekte wie Konvergenzgeschwindigkeit, asymptotische Normalitat, Gesetz vom iterierten Logarithmus etc. auf ahnliche Weise behandelt werden. Der Fall, das die Ableitung der Regressionsfunktionf in dem gesuchten Punktx* gleich Null ist, wird ebenfalls behandelt.
Journal Article•
TL;DR: In this article, the mean and variance of the multinomial distribution were derived in closed form for the moments and compared between Schaffer's [1957] and the exact moments for varying sample size.
Abstract: The mean and variance of — 2 In A for the multinomial distribution are derived in closed form. A comparison is made betweenSchaffer's [1957] approximations to the moments and the exact moments for varying sample size.
TL;DR: The class of estimators for the population mean (i.e. the arithmetic mean of all variate values observed in the sample) is the class {λt0: λ real} as mentioned in this paper.
Abstract: Consider simple random sampling (without replacement) of a fixed size and lett0 be the sample mean, i.e. the arithmetic mean of all variate values observed in the sample. The class {λt0: λ real} of estimators for the population mean (i.e. The arithmetic mean of all variate values) then surely is of interest.
TL;DR: In this article, it was shown that the generalized variance of the autoregressive process is exactly equal to the infinite order generalized variance for the moving average process, for any integer, r, given two processes of order r, one auto-gressive and the other moving average but both with the same parameters.
Abstract: In this paper we give a simple proof of the result that, for any integer,r, given two processes of orderr, one autoregressive and the other moving average but both with the same parameters, then the generalized variance of all ordersk≥2r, for the autoregressive process, is exactly equal to the infinite order generalized variance for the moving average process.
TL;DR: In this article, the Laplace-condition about the possible outcomes of this experiment was shown to be true for both with-replacement and with-no replacement cases of the drawing scheme.
Abstract: Suppose there is a universe which containsN elements,M of which are marked by a special property. From this universe a sample of sizen is drawn without replacement. From the Laplace-condition about the (
) possible outcomes of this experiment it follows that the number of marked elements in the sample is distributed hypergeometrically. It is shown that an inverse of this theorem is true, whereas the analogue inverse for the with-replacement-case is not true. Further some other evident properties of samples are derived from the Laplace-condition for both cases of the drawing scheme. For all cases of possible implications between these properties and the Laplace-condition it is decided if they are true or not.
TL;DR: In this article, a linear multiple decision problem is discussed, where the problem is expressed as a linear combination of a linear MDP and a linear LDP, where each MDP has a set of constraints.
Abstract: A linear multiple decision problem is discussed:
$$\begin{gathered} 0 \leqslant t_i \leqslant a_i i = 1,...,n \hfill \\ 1 - a_0 \leqslant \mathop \sum \limits_{i = 1}^n t_j \leqslant 1 \hfill \\ R_j (t) \leqslant \alpha _j j = 1,...,m \hfill \\ \end{gathered} $$
TL;DR: In this article, the confidence intervals for a shift parameter Δ have been introduced in Metrika 24, 1977, considering intervals of the type [(zr−ξr):max (zr − Δ)):
Abstract: Confidence intervals for a shift parameter Δ have been introduced in Metrika 24, 1977, considering intervals of the type [(zr−ξr):max (zr−ξr)].
TL;DR: In this article, the authors propose a notwendige and hinreichende Bedingung für angegebene Beziehung für the Existenz of the Erwartungswertes.
Abstract: {X (t): t∈R
+} sei ein Punktprozes,H (x) eine konvexe nicht-negative Funktion. Mit Hilfe der „bedingten Wahrscheinlichkeitenp
n
(t) fur genaun Ereignisse (Punkte) im Zeitpunkt punktt unter der Bedingung, das im Zeitpunktt mindestens ein Ereignis eintritt”, wird eine Beziehung formuliert, die fur die Existenz des ErwartungswertesE (H (X (t
0))) notwendig ist. Hat der Punktprozes unabhangige Zuwachse, und erfullt die FunktionH (x) einige weitere Bedingungen, so ist die angegebene Beziehung auch hinreichend fur die Existenz dieses Erwartungswertes. Fur Punktprozesse mit unabhangigen Zuwachsen ergibt sich als unmittelbare Anwendung dieser Aussagen eine notwendige und hinreichende Bedingung fur die Existenz vonE X (t
0)
r
fur reellesr≥1.
TL;DR: With the help of a least favorable pair of densities constructed by minimizing the total variation distance of distributions belonging to the hypotheses and the alternative respectively, it was shown that some well known uniformly most powerful invariant tests are maximin tests.
Abstract: With the help of a least favourable pair of densities constructed by minimizing the total variation distance of distributions belonging to the hypotheses and the alternative respectively, it is shown that some well known uniformly most powerful invariant tests are maximin tests.
TL;DR: In this article, a function f of a finite-state, homogeneous Markov chain is considered and sufficient and necessary conditions are derived that f (X n, n = 1, 2,...) is a homogeneous or inhomogeneous chain.
Abstract: In this paper is considered a functionf of a finite-state, homogeneous Markov chain {X n, n=1,2,...}. Sufficient and necessary conditions are derived that {X n). n=1,2,...} is a homogeneous or inhomogeneous Markov chain. Furthermore the case is considered that {f (X n), n=1,2,...} is Markovian whatever the initial dist