Bartlett corrections in beta regression models

We consider the issue of performing accurate small-sample testing inference in beta regression models, which are useful for modeling continuous variates that assume values in (0,1), such as rates and proportions. We derive the Bartlett correction to the likelihood ratio test statistic and also consider a bootstrap Bartlett correction. Using Monte Carlo simulations we compare the finite sample performances of the two corrected tests to that of the standard likelihood ratio test and also to its variant that employs Skovgaard's adjustment; the latter is already available in the literature. The numerical evidence favors the corrected tests we propose. We also present an empirical application.     

Analytical expressions for the average adjustment interval and mean squared deviation for bounded adjustment schemes

This paper presents analytical expressions for the average adjustment interval and the mean squared deviation from target of the “bounded adjustment” schemes of Box and Luceno (1997a) under the assumption that the disturbances are generated from a double-exponential distribution. The solutions obtained are very close to those computed numerically for normally distributed innovations. This not only demonstrates the robustness of the schemes to the distributional assumptions, but also provides new useful expressions for the average adjustment interval and mean squared deviation from target. Expressions for the characteristic and probability mass functions of the adjustment interval are also given.     

Testing multivariate uniformity: The distance‐to‐boundary method

Given a random sample taken on a compact domain S ? ^d, the authors propose a new method for testing the hypothesis of uniformity of the underlying distribution. The test statistic is based on the distance of every observation to the boundary of S. The proposed test has a number of interesting properties. In particular, it is feasible and particularly suitable for high dimensional data; it is distribution free for a wide range of choices of 5; it can be adapted to the case that the support of S is unknown; and it also allows for one‐sided versions. Moreover, the results suggest that, in some cases, this procedure does not suffer from the well‐known curse of dimensionality. The authors study the properties of this test from both a theoretical and practical point of view. In particular, an extensive Monte Carlo simulation study allows them to compare their methods with some alternative procedures. They conclude that the proposed test provides quite a satisfactory balance between power, computational simplicity, and adaptability to different dimensions and supports.     

Smoking Risks in Spain: Part I—Perception of Risks to the Smoker

Survey evidence for the Spanish population indicates that perceptions of lung cancer risk and life expectancy loss due to smoking are similar to estimates found in the United States. This paper also presents new evidence on the relative lung cancer risk for smokers, the perceived risk of lung disease for smokers, the heart disease risk for smokers, and the relative heart disease risk for smokers, all of which indicate substantial risk perceptions. Risk beliefs are particularly high for younger respondents, but are lower for better educated respondents.     

Underreporting of purchases of port wine

In this paper, we develop a new approach for modelling underreported Poisson counts. The parameters of the model are estimated by Markov chain Monte Carlo simulation. An application to a real data set from a Portuguese marketing survey illustrates the fruitfulness of the approach. We find that purchases of bottles of port wine increase significantly with income class and the size of the household.     

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution.     

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.     

The effect of reparametrization on accelerated lifetime tests

Efficient reliability industrial experiments consist of submitting items to accelerated life tests. It is of interest to obtain measures of the realiability of the devices under the usual working conditions, represented here by the mean lifetime. A practical problem refers to the accuracy of interval estimation of the parameter of interest when the sample size is small or moderate. In this paper, we describe the effect of several reparametrizations on the accuracy of the interval estimation. We propose a reparametrization that leads to accuracy while allowing orthogonality between the parameters. The idea is to consider a logarithmic reparametrization on orthogonal parameters in order to have independent maximum likelihood estimates with good asymptotic normal approximation. The study is illustrated by a data set on an accelerated life test at pressurized containers of Kevlan/Epoxy 49.     

An Experiment on Rational Insurance Decisions

We describe the results of an experiment on decision making in an insurance context. The experiment was designed to test for the underlying rationality of insurance consumers, where rationality is understood in usual economic terms. In particular, using expected utility as the preference function, we test for positive marginal utility, risk aversion, and decreasing absolute risk aversion, all of which are normal postulates for any microeconomic decision context under uncertainty or risk. We find that there the discrepancy from rational decision making increases with the sophistication of the rationality criteria, that irrationality concerning fair premium contracts is uncharacteristically high, and that the slope of absolute risk aversion seems to depend on the format of the insurance contract. This revised version was published online in June 2006 with corrections to the Cover Date.