Information Matrices for Non Full Rank Subsystems

Consider the standard linear model Y=X θ + ε. If the parameter of interest is a full rank subsystem K′θ of mean parameters, the associated information matrix can be defined via an extremal representation. For rank deficient subsystems, Pukelsheim (1993) introduced the notion of generalized information matrices that inherit many properties of the information matrices. However, this notion is not a direct extension of the full rank case in the sense that the definition of the generalized information matrix applied to full rank subsystems does not lead to the usual information matrix. In this paper, we propose a definition of the information matrix via an extremal representation that encompasses the full rank and the non-full rank cases. We also study its properties and show its links with the generalized information matrices.     

Universally optimal designs under mixed interference models with and without block effects

The literature on neighbor designs as introduced by Rees (Biometrics 23:779–791, 1967) is mainly devoted to construction methods, providing few results on their statistical properties, such as efficiency and optimality. A review of the available literature, with special emphasis on the optimality of neighbor designs under various fixed effects interference models, is given in Filipiak and Markiewicz (Commun Stat Theory Methods 46:1127–1143, 2017). The aim of this paper is to verify whether the designs presented by Filipiak and Markiewicz (2017) as universally optimal under fixed interference models are still universally optimal under models with random interference effects. Moreover, it is shown that for a specified covariance matrix of random interference effects, a universally optimal design under mixed interference models with block effects is universally optimal over a wider class of designs. In this paper the method presented by Filipiak and Markiewicz (Metrika 65:369–386, 2007) is extended and then applied to mixed interference models without or with block effects.     

Exploratory study in tourism: designing an initial,qualitative phase of sequenced,mixed methods research

Exploratory studies in the social sciences are being increasingly advocated, particularly in relation to new research themes or when addressing an existing issue from a new perspective. Although exploration is usually the starting point, it is frequently part of a sequence of research stages. However, until recently the actual process of conducting such exploratory research within the leisure and tourism field has received little attention. This is due not just to perceptions that exploration is merely the initial step in a longer research process, but significantly, because there is a lack of guidance on how to conduct such research. This paper argues that when the overall tourism research study involves the use of mixed methods, an initial exploratory stage conducted as part of a sequential research process, requires a systematic approach to achieve a reliable platform for further investigation. The paper shows how and why a systematic research design process in the exploratory stage can enhance the value of studies, when the initial qualitative stage is to be followed by a quantitative phase. Three phases of an exploratory qualitative research design process are identified: preparation, development and refinement. Criteria for assessing the suitability of qualitative data collection techniques are proposed. It is argued that careful attention to the process of designing the initial exploratory qualitative stage constitutes the necessary condition for achieving results that will form a sound basis for the next quantitative sequence of research. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of experiments via a group majorization ordering

This paper generalizes results of Tong (1989) and Shaked and Tong (1992) on comparison of experiments via dependence of normal variables with a common marginal distribution.Research partially supported by Grant KBN.