Detecting fuzzy periodic patterns in futures spreads

This paper extends an optimal frequency domain test for the detection of synchronous patterns in multiple time series to the case of fuzzy patterns, which are not confined to single frequencies or narrow frequency bands. Applying this extension to corn futures with different delivery dates, we obtain significant results only for the spreads between the different contracts but not for the original contracts, which is an indication that spread trading has the advantage of increased predictability.     

An asymptotic approach to progressive censoring

Progressive Type-II censoring was introduced by Cohen (Technometrics 5(1963) 327) and has been the topic of much research. The question stands whether it is sensible to use this sampling plan by design, instead of regular Type-II right censoring. We introduce an asymptotic progressive censoring model, and find optimal censoring schemes for location-scale families. Our optimality criterion is the determinant of the 2×2 covariance matrix of the asymptotic best linear unbiased estimators. We present an explicit expression for this criterion, and conditions for its boundedness. By means of numerical optimization, we determine optimal censoring schemes for the extreme value, the Weibull and the normal distributions. In many situations, it is shown that these progressive schemes significantly improve upon regular Type-II right censoring.     

Repeated chi-square testing

A sequentialized version of the x²; goodness of fit test, called repeated x,²; test, is introduced. The form of the asymptotic distribution of the repeated x² test statistic is given under the null hypothesis as well as under local alternatives. For various numbers of cells Monte Carlo results are given for critical values, power and distribution of stopping time. Finally, the perfor-mance of the repeated and the fixed sample x² test are compared.     

Eine Anwendung der Rayleigh-Verteilung auf ein Problem der Photographie

The problem of blurred photographs due to camera shake is of statistical nature. A short theoretical analysis which leads to the Rayleigh distribution for a statistical treatment of this well known effect is verified by experimental investigations. Based on this distribution, an interesting relationship is found for a simple method for obtaining less blurred photographs.

     

Hermite interpolation polynomials and distributions of ordered data

It is shown that density functions of generalized order statistics can be interpreted as divided differences. Moreover, it turns out that the cumulative distribution functions can be understood as a certain Hermite interpolation polynomial evaluated at the origin. The particular cases of order statistics and record values lead to a Lagrange interpolation polynomial and a Taylor polynomial, respectively.     

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Generalized order statistics from arbitrary distributions and the Markov chain property

The joint and marginal distributions of generalized order statistics based on an arbitrary distribution function are established in terms of the lexicographic distribution function. Furthermore, we show that generalized order statistics and the corresponding number of ties form a two-dimensional Markov chain.