Reversed preservation of stochastic orders for random minima and maxima with applications

In this paper, reversed preservation properties of right spread order, total time on test order and increasing convex (concave) order when taking random minima and maxima are developed. In this context, reversed preservation properties of some ageing concepts are investigated under parallel (series) systems which are composed of a random number of i.i.d. components. Some applications in reliability and economics are given.     

Randomized response techniques for complex survey designs

Singh et al. ([13]) pointed out that the Randomized response (RR) technique proposed by Moors ([9]) is not desirable because it fails to protect the confidentiality of the respondents and they provided two alternative strategies free from the above drawback but limited to SRSWOR sampling only. In this paper, generalization of one of the strategies is provided for complex survey designs, wider class of estimators and for quantitative characteristics. Relative efficiency of the modified strategy is tested through empirical investigations. An erratum to this article is available at .     

An application of cartographic area interpolation to German administrative data

In many situations the applied researcher wishes to combine different data sources without knowing the exact link and merging rule. This paper considers different cartographic interpolation methods for interpolating attributes from German employment office districts to German counties and vice versa. In particular, we apply dasymetric weighting as an alternative to simple area weighting, both of which are based on estimated intersection areas. We also present conditions under which the choice of interpolation method does not matter and confirm the theoretical results with a simulation study. Our application to German administrative data suggests robustness of estimation results of interpolated attributes with respect to the choice of interpolation method. We provide weighting matrices for regional data sources of the two largest German data producers.     

Comparison of different estimation techniques for portfolio selection

The main problem in applying the mean-variance portfolio selection consists of the fact that the first two moments of the asset returns are unknown. In practice the optimal portfolio weights have to be estimated. This is usually done by replacing the moments by the classical unbiased sample estimators. We provide a comparison of the exact and the asymptotic distributions of the estimated portfolio weights as well as a sensitivity analysis to shifts in the moments of the asset returns. Furthermore we consider several types of shrinkage estimators for the moments. The corresponding estimators of the portfolio weights are compared with each other and with the portfolio weights based on the sample estimators of the moments. We show how the uncertainty about the portfolio weights can be introduced into the performance measurement of trading strategies. The methodology explains the bad out-of-sample performance of the classical Markowitz procedures.     

Statistical consulting

The paper and the special issue focus on the activity of statistical consulting and its varieties. This includes academic consulting, consulting to and in industry as well as statistics in public media.     

Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.     

Multi-phase sampling under cost constraints

Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.     

H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.     

Nonconglomerative coherent conditional probabilities in statistical inference

Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference. Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.