Semiparametric Mixtures of Symmetric Distributions

We consider in this paper the semiparametric mixture of two unknown distributions equal up to a location parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. To insure the identifiability of the model, it is assumed that the mixed distribution is zero symmetric, the model being then defined by the mixing proportion, two location parameters and the probability density function of the mixed distribution. We propose a new class of M‐estimators of these parameters based on a Fourier approach and prove that they are ‐consistent under mild regularity conditions. Their finite sample properties are illustrated by a Monte Carlo study, and a benchmark real dataset is also studied with our method.     

Parameter estimation under orthant restrictions

The authors consider the estimation of linear functions of a multivariate parameter under orthant restrictions. These restrictions are considered both for location models and for the Poisson distribution. For these models, situations are characterized for which the restricted maximum likelihood estimator dominates the unrestricted one for the estimation of any linear function of the parameter. The results obtained point directly to the importance of the dimension of the parameter space, the central direction of the cone and its vertex in these cases. Special attention is given to examples, such as the one‐way analysis of variance, where the estimation of individual interesting linear functions of the parameter, as the coordinates and the differences between them, is also treated.     

Kernel density estimators for random fields satisfying an interlaced mixing condition

For a sequence of strictly stationary random fields that are uniformly ρ′-mixing$\rho \prime \mathrm{-}\mathrm{mixing}$ and satisfy a Lindeberg condition, a central limit theorem is obtained for sequences of “rectangular” sums from the given random fields. The “Lindeberg CLT” is then used to prove a CLT for some kernel estimators of probability density for some strictly stationary random fields satisfying ρ′-mixing$\rho \prime \mathrm{-}\mathrm{mixing}$, and whose probability density and joint densities are absolutely continuous.     

Estimating the stability of census-based racial/ethnic classifications: the case of Brazil

This study presents a method of estimating the degree to which people change their racial/ethnic identity from one census enumeration to another. The technique is applied to the classification of skin colour in Brazil (white, black, brown, yellow). For the period 1950-80, the findings show a deficit of 38 per cent in the black category and a gain of 34 per cent in the brown category, suggesting that a large proportion of individuals who declared themselves black in 1950 reclassified themselves as brown in 1980. Estimates for 1980-90, adjusted for the effects of international migration, reveal a similar pattern, although the magnitude of colour reclassification may have declined somewhat during the 1980s. Procedures to determine the stability of racial/ethnic identity produce data useful to recent policy initiatives that rely on demographic censuses to measure changes in the status of minority groups in less developed countries.     

The Well-Being of 12 - to 16-Year-Old Adolescents and their Parents: Results from 1999 to 2003 Spanish Samples

This study adopts satisfaction with life as a whole and satisfaction with specific life domains as indicators to analyse the relationships between the well-being of 12 to 16-year-old adolescents and some related constructs such as self-esteem, perceived control and perceived social support. Well-being indicators from a 2003 Spanish sample using an 11-point scale (N = 1,634) are compared with an equivalent 1999 Spanish sample using a 5-point scale (N = 1,618). The different results obtained from the 2003 sample with a Principal Component Analysis (PCA) using a shorter and a longer list of life domains are also discussed. A sub-sample of the adolescents’ results from the 2003 sample are compared with their parents’ answers, using the same well-being indicators. Using a list of 8 life domains, and despite the change of scale used, overall results show no relevant changes in adolescents’ satisfaction with life domains between 1999 and 2003 in Spain and are in agreement with normative data expected from western societies [Cummins: 1998, Social Indicators Research 43, pp. 307–334; Cummins et al.: 2001, Australian Unity Well-being Index (Australian Centre on Quality of Life, Deakin University, Melbourne)]. Adolescents’ overall life satisfaction has been shown to correlate consistently with the other well-being related constructs. However, it clearly decreases with age over the period studied. The results also show that increasing the list of life domains has a major impact on the structure of the results obtained. When we compare results from parents with those from their own child, outstanding differences in well-being appear between generations: few domain satisfaction dimensions show significant correlation between parents and children and more than 20% of the population studied shows high discrepancies in the answers in four domains.     

Relationships Between Parents’ And Children’s Salient Values For Future And Children’s Overall Life Satisfaction. A Comparison Across Countries

In this paper, a model is set forth relating (a) overall life satisfaction of children to children’s values and (b) children’s values to parents’ values. Using confirmatory factor analysis models three dimensions of values (materialistic values, capacities and knowledge values and interpersonal relationship values) consistently emerged in 5 countries (Brazil, South Africa, Norway, Spain and India) for both parents and children. There was a considerable amount of missing data, mainly because the parent’s questionnaire was often not returned. Full information maximum likelihood estimators with missing data were thus used.Multiple-group analyses were next performed to assess factor invariance of the three value dimensions across the five countries for both parents and children. This implies testing the equality of factor loadings and intercepts across groups. This equality is required to ensure that factors have the same interpretation in all groups, which is necessary when comparing any aspect of the factor distribution across groups.The only two countries for which the interpretation of value dimensions was invariant for both parents and children were Brazil and Spain. The results of other countries could thus not be compared. Multiple-group structural equation models revealed that both parents and children scored higher on most values in Brazil than in Spain. In both countries, each child value dimension was only significantly predicted by the same value dimension of the parents. R-squares were in the 4–12% range and slightly higher in Brazil. The only value dimension that had some effect on overall life satisfaction was capacities and knowledge, which was so in both countries.Acknowledgements are due to the country project directors and their associates Per Egil Mjaavatn (Norwegian University of Science and Technology, Trondheim, Norway), Usha Nayar (Tata Institute of Social Sciences, India), Irene Rizzini (Pontifícia Universidade Católica do Rio de Janeiro, Brazil), Rose September (Western Cape University, South Africa) and Ferran Casas (Catalan Network of Child Researchers – XCIII – in co-operation with the University of Girona, Spain) for permitting us to use part of their project and to Childwatch International, Oslo, for sponsorship.     

Parametric Bayesian inference for Y-linked two-sex branching models

A Y-linked two-sex branching process with blind choice is a suitable model for analyzing the evolution of the number of carriers of two alleles of a Y-linked gene in a two-sex monogamous population where each female chooses her partner from among the male population without caring about his type (i.e., the allele he carries). This work focuses on the development of Bayesian inference for this model, considering a parametric framework with the reproduction laws belonging to the power series family of distributions. A sample is considered given by the observation of the total number of females and males (regardless of their types) up to some generation as well as the number of each type of male in the last generation. Using a simulation method based on the Gibbs sampler, we approximate the posterior distributions of the main parameters of this model. The accuracy of the procedure based on this sample is illustrated by way of a simulated example.     

Taxes and Women in the Labour Force in a Southern European Country: The Case of Portugal

On looking at the female labour supply in Europe, it is immediately noticed that there is a large variation among countries. One possible explanation for this fact is that different countries have different tax policies, leading to variations in incentive and costs. This has been investigated in papers such as that of Gustafsson (1992a,b) for countries such as Germany and Sweden. The same exercise has been performed by the present authors for a low-income, southern European country, Portugal, which has one of the highest rates of female participation (out of line with neighbouring countries). Female labour supply does not seem to be very sensitive to fiscal policies, as those policies have only a small influence on the take-home wage. This result appears to be independent of the fact that the female labour supply shows a higher elasticity to wages than that which has been reported for other countries. The present authors also show that Portuguese women contribute a much larger proportion of family earnings than do their counterparts in Sweden and Germany, and that the Portuguese fiscal system is rather neutral. Further studies with data from other countries are needed in order to shed more light on the issue of tax harmonization.