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The estimation of a latent construct is a crucial issue when a phenomenon is a consequence of the joint occurrence of multiple features. Several techniques for estimating latent phenomena are proposed in literature, but since the variable under study is unobservable, and the law by which the features combine together is unknown, comparison of results obtained with different methods is achieved through simulation‐based analyses. The latent construct is measured by a multidimensional index (MI), which determines a ranking among the observations. It is therefore relevant to assess the reliability of the methods by which such rankings are produced. In this paper, we propose two procedures evaluating the assessment of latent constructs and the corresponding rankings. The first one is a simulation‐based mean square error, which evaluates the MI accuracy, while the second one uses a simulation average split ranking index, which assesses its reliability. Both methodologies are illustrated with an application to the assessment of the urban sustainability, and three methodologies of building MIs are compared: the first one based on structural equation models; the second one based on principal component analysis; and the third one that uses an equal weight method. [ABSTRACT FROM AUTHOR]

Immigration flows and social inequalities reflect increased social and multi‐ethnic segregation in contemporary urban Europe. For a better understanding of these processes, the present study investigates the main strengths of the multi‐group residential indices, testing sensitivity and reliability under different metropolitan contexts in five European countries. These indices focus on different research dimensions and approach multi‐group residential segregation conceptually and mathematically in a different way. A multivariate exploratory data analysis was adopted to classify the observed segregation patterns into a few homogeneous types and to delineate the multivariate relationship between the indices. The results of principal component analysis demonstrate that the indices assessing uniformity and disproportionality of the social groups analysed (H and D) contribute largely to the diversification in today's multi‐ethnic communities, clarifying the importance of the dimension of evenness. Our results highlight how segregation is more evident in economically disadvantaged metropolitan regions with high levels of social vulnerability. [ABSTRACT FROM AUTHOR]

The theory of value has been based ever since Adam Smith on the idea that the market prices of commodities, those at which actual trade takes place, gravitate around a central position known as natural prices. This article seeks to develop a statistical idea of the process in question and suggests in particular that market prices can be said to gravitate around natural prices if the probability of their means being very close to natural prices after t observations tends to 1 as t tends to infinity. A set of possible conditions leading to that result is also presented. [ABSTRACT FROM AUTHOR]