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.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Imitation of succesful behavior in Cournot markets

In an experimental standard Cournot Oligopoly we test the importance ofmodels of behavior characterized by imitation of succesful behavior. Wefind that the players appear to the rather reluctant to imitate.

The risk of divorce and household saving behavior

We analyze the impact of an increase in the risk of divorce on the savingbehaviour of married couples. From a theoretical perspective, the expected sign of theeffect is ambiguous. We take advantage of the legalization of divorce in Ireland in 1996as an exogenous increase in the likelihood of marital dissolution. We analyze the savingbehaviour over time of couples who were married before the law was passed. We proposea difference-in-differences approach where we use as comparison groups either marriedcouples in other European countries (not affected by the law change), or Irish familieswho did not experience a significant increase in the expected risk of divorce (such as veryreligious families, or single individuals). Our results suggest that the increase in the riskof divorce brought about by the law was followed by an increase in the propensity to saveof married couples, consistent with a rise in precautionary savings interpretation. Anincrease in the risk of marital dissolution of about 40 percent led to a 7 to 13 percent risein the proportion of married couples reporting positive savings.

A theory of reference-dependent behavior

Extensive field and experimental evidence in a variety of environments show that behavior depends on a reference point. This paper provides an axiomatic characterization of this dependence. We proceed by imposing gradually more structure on both choice correspondences and preference relations, requiring increasingly higher levels of rationality, and freeing the decision-maker from certain types of inconsistencies. The appropriate degree of behavioral structure will depend on the phenomenon that is to be modeled. Lastly, we provide two applications of our work: one to model the status-quo bias, and another to model addictive behavior.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Ethical differentiation and market behavior: An experimental approach

Does ethical differentiation of products affect market behavior? We examined this issue in triopolistic experimental markets where producers set prices. One producer s costs were higher than the others. In two treatments, the additional costs were attributed tocompliance with ethical guidelines. In the third, no justification was provided. Manyparticipants playing the role of consumers reduced their experimental gains by purchasing the ethically differentiated product at a higher price whether or not they knew the amount of extra cost. Individual differences were important (students of business/economics paid smaller premia than others). Finally, we speculate about the observed demand function for ethics and emphasize the use of experimental methodology to complement empirical studies designed to assess the potential market for ethically differentiated products.

Weak and strong altruism in traitgGroups: Reproductive suicide, personal fitness and expected value

A simple variant of trait group selection, employing predators as themechanism underlying group selection, supports contingent reproductivesuicide as altruism (i.e., behavior lowering personal fitness whileaugmenting that of another) without kin assortment. The contingentsuicidal type may either saturate the population or be polymorphicwith a type avoiding suicide, depending on parameters. In addition tocontingent suicide, this randomly assorting morph may also exhibitcontinuously expressed strong altruism (sensu Wilson 1979) usuallythought restricted to kin selection. The model will not, however,support a sterile worker caste as such, where sterility occurs beforelife history events associated with effective altruism; reproductivesuicide must remain fundamentally contingent (facultative sensu WestEberhard 1987; Myles 1988) under random assortment. The continuouslyexpressed strong altruism supported by the model may be reinterpretedas probability of arbitrarily committing reproductive suicide, withoutbenefit for another; such arbitrary suicide (a "load" on "adaptive"suicide) is viable only under a more restricted parameter spacerelative to the necessarily concomitant adaptive contingent suicide.

Human nature and institutional analysis

This essay reviews some findings in cognition sciences and examines their consequences for the analysis of institutions. It starts by exploring how humans specialization in producing knowledge ensures our success in dominating the environment but also changes fast our environment. So fast that it did not give time to natural selection to adapt our biology, causing it to be potentially maladapted in important dimensions. A main function of institutions is therefore to fill the gap between the demands of our relatively new environment and our biology, still adapted to our ancestral environment as hunter-gatherers. Moreover, institutions are built with the available elements, which include our instincts. A deeper understanding of both aspects, their adaptive function and this recruitment of ancestral instincts, will add greatly to our ability to manage institutions.

On the complexity of rationalizing behavior

We study the complexity of rationalizing choice behavior. We do so by analyzing two polar cases, and a number of intermediate ones. In our most structured case, that is where choice behavior is defined in universal choice domains and satisfies the "weak axiom of revealed preference," finding the complete preorder rationalizing choice behavior is a simple matter. In the polar case, where no restriction whatsoever is imposed, either on choice behavior or on choice domain, finding the complete preordersthat rationalize behavior turns out to be intractable. We show that the task of finding the rationalizing complete preorders is equivalent to a graph problem. This allows the search for existing algorithms in the graph theory literature, for the rationalization of choice.

Adaptive dynamics and the implementation problem with complete information

This paper studies the equilibrating process of several implementationmechanisms using naive adaptive dynamics. We show that the dynamics convergeand are stable, for the canonical mechanism of implementation in Nash equilibrium.In this way we cast some doubt on the criticism of ``complexity'' commonlyused against this mechanism. For mechanisms that use more refined equilibrium concepts,the dynamics converge but are not stable. Some papers in the literatureon implementation with refined equilibrium concepts have claimed that themechanisms they propose are ``simple'' and implement ``everything'' (incontrast with the canonical mechanism). The fact that some of these ``simple''mechanisms have unstable equilibria suggests that these statements shouldbe interpreted with some caution.

Europe and the Petersberg Tasks – Nation-State behavior through the prism of Strategic Culture

Les missions Petersberg són l'operatiu militar més ambiciós organitzat per la Unió Europea en el desenvolupament de la CSDP, Política Europea de Seguretat i Defensa. Amb l'objectiu d'aconseguir una organització efectiva y funcional d'aquestes missions, és desitjable que les cultures estratègiques dels diferents Estats membres siguin, en gran mesura, compatibles en benefici d'una cultura estratègica europea amb directrius clares. Aquest estudi compara les cultures estratègiques d'Alemanya, el Regne Unit i França en referència al seu nivell de compatibilitat contrastant-les amb dos casos recents, exemples paradigmàtics de cultures estratègiques integrals. D'aquesta manera, pretenem descriure les circumstàncies en què es desenvolupen les missions Petersberg.

A qualitative study of the impact of electronic journals on scholarly information behavior

A qualitative study of the impact of electronic journals on the information behavior of academics at Catalan universities shows that academics now read more, and more widely. However, their reading is becoming more superficial; they are compelled to improve their discrimination skills in order to decide what to read in more depth. The electronic accessibility of journals means that academics now make fewer library visits. Web browsing and TOC e-mail alerts are replacing physical browsing, and searching is a very popular option for keeping up to date with developments. Internet search engines, especially Google and Google Scholar, are becoming important sources of information for academics. However, they face problems in managing their personal scientific information.

Time-scale and other invariants of integrative mechanical behavior in living cells.

In dealing with systems as complex as the cytoskeleton, we need organizing principles or, short of that, an empirical framework into which these systems fit. We report here unexpected invariants of cytoskeletal behavior that comprise such an empirical framework. We measured elastic and frictional moduli of a variety of cell types over a wide range of time scales and using a variety of biological interventions. In all instances elastic stresses dominated at frequencies below 300 Hz, increased only weakly with frequency, and followed a power law; no characteristic time scale was evident. Frictional stresses paralleled the elastic behavior at frequencies below 10 Hz but approached a Newtonian viscous behavior at higher frequencies. Surprisingly, all data could be collapsed onto master curves, the existence of which implies that elastic and frictional stresses share a common underlying mechanism. Taken together, these findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation. Moreover, these observations are consistent with the hypothesis that the cytoskeleton of the living cell behaves as a soft glassy material, wherein cytoskeletal proteins modulate cell mechanical properties mainly by changing an effective temperature of the cytoskeletal matrix. If so, then the effective temperature becomes an easily quantified determinant of the ability of the cytoskeleton to deform, flow, and reorganize.