A Note on Whittle's Likelihood

The approximate likelihood function introduced by Whittle has been used to estimate the spectral density and certain parameters of a variety of time series models. In this note we attempt to empirically quantify the loss of efficiency of Whittle's method in nonstandard settings. A recently developed representation of some first-order non-Gaussian stationary autoregressive process allows a direct comparison of the true likelihood function with that of Whittle. The conclusion is that Whittle's likelihood can produce unreliable estimates in the non-Gaussian case, even for moderate sample sizes. Moreover, for small samples, and if the autocorrelation of the process is high, Whittle's approximation is not efficient even in the Gaussian case. While these facts are known to some extent, the present study sheds more light on the degree of efficiency loss incurred by using Whittle's likelihood, in both Gaussian and non-Gaussian cases.     

Accuracy of Power-Divergence Statistics for Testing Independence and Homogeneity in Two-Way Contingency Tables

The small-sample accuracy of seven members of the family of power-divergence statistics for testing independence or homogeneity in contingency tables was studied via simulation. The likelihood ratio statistic G ² and Pearson's X ² statistic are among these seven members, whose behavior was studied at nominal test sizes of.01 and.05 with marginal distributions that could be uniform or skewed and with a set of sample sizes that included sparseness conditions as measured through table density (i.e., the ratio of sample size to number of cells). The likelihood ratio statistic G ² rejected the null hypothesis too often even with large table density, whereas Pearson's X ² was sufficiently accurate and only presented a minor misbehavior when table density was less than two observations/cell. None of the other five statistics outperformed Pearson's X ². A nonasymptotic variant of X ² solved the minor inaccuracies of Pearson's X ² and turned out to be the most accurate statistic for testing independence or homogeneity, even with table densities of one observation/cell. These results clearly advise against the use of the likelihood ratio statistic G ².     

Bayesian robustness of credible regions in the presence of nuisance parameters

The problem of finding the most robust γ-level credible region for the parameter of interest in the presence of a nuisance parameter, with respect to a class of ε-contaminated priors, is studied. The case of arbitrary con-taminations is first analyzed; it is proved that the most robust region for the parameter of interest is theγ-level highest marginal likelihood region (forγ ≥ 0.5). Then, the result is extended to any measurable (not necessarily one-to-one) function of the parameter. Finally, the case of contaminations assigning fixed probabilities to the sets of a partition of the parameter space is analyzed and a partial result is given.     

Have I seen you before? Principles of Bayesian predictive classification revisited

A general inductive Bayesian classification framework is considered using a simultaneous predictive distribution for test items. We introduce a principle of generative supervised and semi-supervised classification based on marginalizing the joint posterior distribution of labels for all test items. The simultaneous and marginalized classifiers arise under different loss functions, while both acknowledge jointly all uncertainty about the labels of test items and the generating probability measures of the classes. We illustrate for data from multiple finite alphabets that such classifiers achieve higher correct classification rates than a standard marginal predictive classifier which labels all test items independently, when training data are sparse. In the supervised case for multiple finite alphabets the simultaneous and the marginal classifiers are proven to become equal under generalized exchangeability when the amount of training data increases. Hence, the marginal classifier can be interpreted as an asymptotic approximation to the simultaneous classifier for finite sets of training data. It is also shown that such convergence is not guaranteed in the semi-supervised setting, where the marginal classifier does not provide a consistent approximation.     

Income Inequality Indices Interpreted as Measures of Relative Deprivation/Satisfaction

This paper considers different ways of making comparisons between individuals in terms of deprivation and/or satisfaction. This allows the Gini index, the Bonferroni index and the De Vergottini index to be interpreted as social deprivation measures as well as social satisfaction measures. The inequality measures that belong to the ?? family, or linear combinations of them, are obtained when using different weighting schemes to average the deprivation and satisfaction associated with each income level. Particularly, the generalised Gini indices (Yitzhaki, Int Econ Rev 24:617?C628 in 1983), the indices proposed by Aaberge (J Econ Inequal 5(3):305?C322, 2007) or those proposed by Imedio-Olmedo et al. (J Public Econ Theory 13(1):97?C124, 2011) can be used to evaluate social deprivation or social satisfaction in an income distribution.     

Family Trajectories and Terminations in Conditional Cash Transfer Programs: The Case of Chile's Ethical Family Wage Program

ABSTRACT

On an international scale, conditional cash transfer (CCT) programs have rapidly expanded. Since their boom in the 1990s newer modalities have emerged, incorporating some innovative components. The following study sought to examine one particular CCT program heralded as innovative due to its psychosocial and socio employment accompaniment components: Chile's Ethical Family Wage program. Utilizing administrative data from the Ministry of Social Development this exploratory study sought to examine family trajectories in the program with a particular focus on those families who were terminated from the program due to not meeting conditionalities. Findings from the study indicate that the program deviates sharply from its theoretical implementation. Furthermore, the probabilities of program termination increased in those families headed by younger adults, female and single-headed households, households with higher levels of education as well as larger families. However, a greater number of children decreased the probabilities of program termination as was homeownership. Implications of the findings for policy and practice are discussed.     

Copper mining productivity: Lessons from Chile

Chile represents almost one third of the world’s copper production. Mining is one of the main industries that contributes to our country’s development with resources and is globally recognized. Due to the end of the commodity cycle, improving productivity will be a key variable in mining performance in incoming years. This paper studies mining productivity in Chile by relying on two indicators: measure of the total factor productivity (TFP) using the traditional Solow methodology, and labor productivity. Since 2000, we found a decrease in TFP, explained mainly by the participation of capital as well as diverse factor adjustments to labor and capital inputs. Average labor productivity also decreases 42% from 1999 to 2010, a decrease explained by four determinants: real mining wages, electricity prices, copper prices and mineral grade. Since 2010, average labor productivity has increased 30%, and there is also an opportunity for additional improvement by reducing energy costs as well as by aligning productivity and labor performances.     

A menu on output gap estimation methods

This paper presents a review of output gap modeling techniques, which are of special interest for policy making institutions. We distinguish between univariate – which estimate trend output on the basis of actual output, without taking into account the information contained in other variables –, and multivariate methods — which incorporate useful information on some other variables, based on economic theory. We present the main advantages and drawbacks of the different methods.     

Asymmetric matrix-valued covariances for multivariate random fields on spheres

ABSTRACT

Matrix-valued covariance functions are crucial to geostatistical modelling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overly restrictive and has been considered as unrealistic for most of the real data applications. Despite of that, the literature on asymmetric covariance functions has been very sparse. In particular, there is some work related to asymmetric covariances on Euclidean spaces, depending on the Euclidean distance. However, for data collected over large portions of planet Earth, the most natural spatial domain is a sphere, with the corresponding geodesic distance being the natural metric. In this work, we propose a strategy based on spatial rotations to generate asymmetric covariances for multivariate random fields on the d-dimensional unit sphere. We illustrate through simulations as well as real data analysis that our proposal allows to achieve improvements in the predictive performance in comparison to the symmetric counterpart.