Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Body size, activity, employment and wages in Europe: A first approach

This paper examines the associations between obesity, employment status and wages for several European countries. Our results provide weak evidence that obese workers are more likely to be unemployed or tend to be more segregated in self-employment jobs than their non-obese counterparts. We also find difficult to detect statistically significant relationships between obesity and wages. As previously reported in the literature, the association between obesity, unemployment and wages seems to be different for men and women. Moreover, heterogeneity is also found across countries. Such heterogeneity can be somewhat explained by some labor market institutions, such as the collective bargaining coverage and the employer-provided health insurance.

Openness, government size and the terms of trade

This paper investigates the relationship between trade openness and the size of government, both theoretically and empirically. We show that openness can increase the size of governments through two channels: (1) a terms of trade externality, whereby trade lowers the domestic cost of taxation and (2) the demand for insurance, whereby trade raises risk and public transfers. We provide a unified framework for studying and testing these two mechanisms. First, we show how their relative strength depends on a key parameter, the elasticity of substitution between domestic and foreign goods. Second, while the terms of trade externality leads to inefficiently large governments, the increase in public spending due to the demand for insurance is optimal. We show that large volumes of trade may result in welfare losses if the terms of trade externality is strong enough while small volumes of trade are always beneficial. Third, we provide new evidence on the positive association between openness and the size of government and test whether it is consistent with the terms of trade externality or the demand for insurance. Our findings suggest that the positive relationship is remarkably robust and that the terms of trade externality may be the driving force behind it, thus raising warnings that globalization may have led to inefficiently large governments.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

The size and distribution of donations: Effects of numbers of potential recipients

Whereas much literature exists on choice overload, little is known about effects of numbers of alternatives in donation decisions. How do these affect both the size and distribution of donations? We hypothesize that donations are affected by the reputation of recipients and increase with their number, albeit at a decreasing rate. Allocations to recipients reflect different concepts of fairness equity and equality. Both may be employed but, since they differ in cognitive and emotional costs, numbers of recipients are important. Using a cognitive (emotional) argument, distributions become more uniform (skewed) as numbers increase. In a survey, respondents indicated how they would donate lottery winnings of 50 Euros. Results indicated that more was donated to NGO s that respondents knew better. Second, total donations increased with the number of recipients albeit at a decreasing rate. Third, distributions of donations became more skewed as numbers increased. We comment on theoretical and practical implications.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Ús de minicasos a les classes expositives de psicologia

L’assoliment de l’Espai Europeu d’Educació Superior implica nous rols per a professorsi alumnes i la introducció de noves metodologies docents. En aquest article es presenta unaexperiència d’innovació en la docència de la Psicologia consistent en la incorporació deminicasos a les classes expositives de l’assignatura troncal i anual “Avaluació Psicològica” desegon curs de la llicenciatura de Psicologia. S’exposa el procediment i s’analitza l’opinió delsestudiants respecte a la utilitats dels minicasos per incrementar l’atenció, l’interès i lacomprensió de l’assignatura

The great diversification and its undoing

We investigate the hypothesis that macroeconomic fluctuations are primitively theresults of many microeconomic shocks, and show that it has significant explanatorypower for the evolution of macroeconomic volatility. We define ?fundamental? volatilityas the volatility that would arise from an economy made entirely of idiosyncratic microeconomicshocks, occurring primitively at the level of sectors or firms. In its empiricalconstruction, motivated by a simple model, the sales share of different sectors vary overtime (in a way we directly measure), while the volatility of those sectors remains constant.We find that fundamental volatility accounts for the swings in macroeconomicvolatility in the US and the other major world economies in the past half century. Itaccounts for the ?great moderation? and its undoing. Controlling for our measure offundamental volatility, there is no break in output volatility. The initial great moderationis due to a decreasing share of manufacturing between 1975 and 1985. The recentrise of macroeconomic volatility is due to the increase of the size of the financial sector.We provide a model to think quantitatively about the large comovement generated byidiosyncratic shocks. As the origin of aggregate shocks can be traced to identifiablemicroeconomic shocks, we may better understand the origins of aggregate fluctuations.

Growth and reproduction of the dolphinfish (Coryphaena equiselis and Coryphaena hippurus) in the Canary Islands, Central-East Atlantic (preliminary results)

The size, growth and spawning characteristics of pompano dolphin (N=150) and common dolphinfish (N=36) caught off the Canary Islands between May and September 1995 and between July and September 1996 were examined. Fork length (FL) of pompano dolphin was in the range 28.3-62.8 cm. In 1995, the mean length increased significantly from June to September. However, in 1996, the mean length was significantly larger in July than in September. The overall length-weight relationship was W=0.0287*FL2.774 (r=0.97), while these relationships by sex were as follows: W=0.031*FL2.758 (r=0.98) and W=0.0282*FL2.776 (r=0.97), for males and females respectively. Spawning takes place at the beginning of the Summer (June-July). All the individuals obtained showed developing gonads, but females showed a higher gonadosomatic index (GSI) than males. The highest GSI values were obtained in June (x- =3.10±1.73), and decreased progressively towards the end of the season (September), when the average of this index was x- = 1.86±0.87. Similarly, the condition index decreased significantly from June to September. The proportion of females was always significantly higher than males, except in July 1996 when it was 1:1. There was a high correspondence between growth rates determined by annuli scale interpretation and modal progression analysis. According to scale annuli interpretation, the individuals caught showed more than five age classes. However, there are doubts about age assignation from scales. Fork length of common dolphinfish was in the range of 76.5-103.0 cm. The length-weight relationships obtained for all the specimens caught was W=0.00095FL3.527 (r=0.96), while these relationships by sex were as follows: W=0.00398FL3.222 (r=0.94) and W=0.01656FL2.873 (r=0.91), for males and females respectively. Spawning probably takes place at the beginning of the Summer. All the individuals obtained showed developing gonads, although the GSI of females were higher than males. The highest GSI values were obtained in June (x- =5.50±2.17). In the same way, the condition index decreased from May to June. The proportion of females was always slightly higher than males (1:1.4), but the ratio was not significantly different from 1:1

Labor market heterogeneity and the aggregate matching function

The matching function -a key building block in models of labor market frictions- impliesthat the job finding rate depends only on labor market tightness. We estimate such amatching function and find that the relation, although remarkably stable over 1967-2007,broke down spectacularly after 2007. We argue that labor market heterogeneities are notfully captured by the standard matching function, but that a generalized matching functionthat explicitly takes into account worker heterogeneity and market segmentation is fullyconsistent with the behavior of the job finding rate. The standard matching function canbreak down when, as in the Great Recession, the average characteristics of the unemployedchange too much, or when dispersion in labor market conditions -the extent to which somelabor markets fare worse than others- increases too much.

On the Chern classes and the Euler characteristic for nonsingular complete intersections

It is shown that Hirzebruch's result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in PN(C), is also valid for any nonsingular complete intersection. Then rela- tions between Euler characteristic, class and Milnor number are pointed out.