Spiridon Penev

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PETER HALL, SPIRIDON PENEV, GE RARD KERKYACHARIAN and DOMINIQUE PICARD Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia School of Mathematics, University of NSW, Sydney, NSW 2052, Australia Faculte Mathematiques et Informatiques, Universite de Picardie, 33 rue Saint-Leu, 80039 Amiens Cedex 01,(More)
We derive representations of higher order dual measures of risk in Lp spaces as suprema of integrals of Average Values at Risk with respect to probability measures on (0, 1] (Kusuoka representations). The suprema are taken over convex sets of probability measures. The sets are described by constraints on the dual norms of certain transformations of(More)
Unlike a substantial part of reliability literature in the past, this article is concerned with weighted combinations of a given set of congeneric measures with uncorrelated errors. The relationship between maximal coefficient alpha and maximal reliability for such composites is initially dealt with, and it is shown that the former is a lower bound of the(More)
In covariance structure modelling, the non-centrality parameter of the asymptotic chi-squared distribution is typically used as an indicator of asymptotic power for hypothesis tests. When a latent linear regression is of interest, the contribution to power by the maximal reliability coefficient, which is associated with used latent variable indicators, is(More)
A procedure for point and interval estimation of maximal reliability of multiple-component measuring instruments in multi-level settings is outlined. The approach is applicable to hierarchical designs in which individuals are nested within higher-order units and exhibit possibly related performance on components of a given homogeneous scale. The method is(More)
A linear combination of a set of measures is often sought as an overall score summarizing subject performance. The weights in this composite can be selected to maximize its reliability or to maximize its validity, and the optimal choice of weights is in general not the same for these two optimality criteria. We explore several relationships between the(More)
Suppose we observe a geometrically ergodic Markov chain with a parametric model for the marginal, but no (further) information about the transition distribution. Then the empirical estimator for a linear functional of the joint law of two successive observations is no longer efficient. We construct an improved estimator and show that it is efficient. The(More)