Identifiability and Comparison of Estimation Methods on Weibull Mixture Models

In this article, the finite mixture model of Weibull distributions is studied, the identifiability of the model with m components is proven, and the parameter estimators for the case of two components resulted by several algorithms are compared. The parameter estimators are obtained with maximum likelihood performing calculations with different algorithms: expectation-maximization (EM), Fisher scoring, backfitting, optimization of k-nearest neighbor approach, and random walk algorithm using Monte Carlo simulation. The Akaike information criterion and the log-likelihood value are used to compare models. In general, the proposed random walk algorithm shows better performance in mean square error and bias. Finally, the results are applied to electronic component lifetime data.     

Sources of error in reported childlessness in a continuous British household survey

A recent investigation of the British General Household Survey (GHS) found substantial over-reporting of childlessness in recent years, particularly at older ages. We examine the phenomenon in further detail and find that the principal cause was change in survey procedures. To some extent the bias can be corrected for by using information on own children in the household. Revised fertility histories give period estimates of total fertility that are in close agreement with national vital registration statistics, unlike those based on original fertility histories of recent years. Misreporting in fertility histories dates primarily from administrative changes in the GHS in the years 1998-2000, and particularly from 2003, when the option of laptop self-completion (CASI) was introduced for reporting demographic histories.     

Employing the Components of the Human Development Index to Drive Resources to Educational Policies

A new form of composition of the indicators employed to generate the United Nations Human Development Index (HDI) is presented here. This form of composition is based on the assumption that random errors affect the measurement of each indicator. This assumption allows for replacing the vector of evaluations according to each indicator by vectors of probabilities of being the best or the worst according to such attribute. The probabilistic composition of such probabilities of preference according to each indicator into probabilities of being the best or the worst according to all of them generates indices that may unveil, on one hand, performances to be followed and, on the other hand, extreme conditions that an additive composition would hide. Differences between the results of application of the diverse forms of composition are examined in the case of the HDI and in the case of the districts version of the HDI employed to compare Brazilian municipalities. It is verified that the smallest correlation between the education enrolment rate and the other indicators in the Brazilian case enlarges such differences.     

The effect of variability and carryover on average bioequivalence assessment: a simulation study

The purpose of this study was to evaluate the effect of residual variability and carryover on average bioequivalence (ABE) studies performed under a 22 crossover design. ABE is usually assessed by means of the confidence interval inclusion principle. Here, the interval under consideration was the standard 'shortest' interval, which is the mainstream approach in practice. The evaluation was performed by means of a simulation study under different combinations of carryover and residual variability besides of formulation effect and sample size. The evaluation was made in terms of percentage of ABE declaration, coverage and interval precision. As is well known, high levels of variability distort the ABE procedures, particularly its type II error control (i.e. high variabilities make difficult to declare bioequivalence when it holds). The effect of carryover is modulated by variability and is especially disturbing for the type I error control. In the presence of carryover, the risk of erroneously declaring bioequivalence may become high, especially for low variabilities and large sample sizes. We end up with some hints concerning the controversy about pretesting for carryover before performing ABE analysis.     

On Terrel's characterization of uniform distribution

Terrel (1983) (The Annals of Probability, Vol. 11, No. 3, 823–826) showed that the coefficient of correlation between the smaller and larger of a sample of size two is at most one-half, and this upper bound is attained only for continuous uniform distributions. His proof is of computational nature and is based on the properties of Legendre polynomials. We give an easier proof of Terrel's characterization and we show how our method can be used for obtaining sharper bounds within the class of discrete distributions onN points and also a characterization of the equidistant uniform distribution.     

Dynamics of HDI Index: Temporal Dependence Based on D-vine Copulas Model for Three-Way Data

The HDI (Human Development Index) is a widely used index based on the average of measures of health, education, and income. It assesses the progress of countries worldwide. The publicly available data set associated with the HDI can be seen as a table with 3 dimensions (three-way table): countries, indexes regarding progress, and years (from 2010 to 2018). Thus, modeling the serial dependence structure of this type of intricate three-way tables is a challenge. D-vine copulas are a special class of multivariate copulas that are particularly suited for modeling serial dependence. This work aims to assess the evolution of the dependence relationship between the indexes of the HDI data set over time through D-vine copulas, which has not been fully used before in the area, as far as we are concerned. We tested our approach to European and African countries and compare their results.

     

Measuring labour market segmentation for a comparative analysis among countries

This article raises one main question in a comparative analytical exercise between two countries in different continents, Spain and Argentina. To what extent does labour market segmentation generate similar dynamics of structuring of labour inequalities in two countries with different socio-economic contexts and social models, and which aspects are specific to each country? The article is the first an analytical work aimed at comparing European and Latin American countries from the theoretical perspective of labour market segmentation. We set two main objectives. The first was to construct an analysis model to study inequalities in the labour market in comparative terms between Europe and Latin America, taking as a reference Spain and Argentina. To this end, demand and supply variables were combined from an employment perspective. We sought to corroborate the general hypothesis that there is no single labour market that adjusts supply and demand, but that several segments can be expected to structure hierarchical positions in the labour market in line with specific labour supply profiles. We expected to obtain a high correspondence between the employment segments of the two countries, despite the contextual and socio-historical differences. The second objective was to propose a methodology to obtain two synthetic measures of labour market segmentation: first, a categorical measurement through a typology constructed from hierarchical positions and profiles using multivariate techniques (combining multiple correspondence factor analysis [MCA] and cluster analysis [CLA]); and second, a continuous measurement based on the results of factor analysis, resulting in a composite indicator of labour inequality.

     

Improved inference for MCP-Mod approach using time-to-event endpoints with small sample sizes

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.