A new method for constructing exact tests without making any assumptions

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes.This method separates the search for an exact test from the goal to create a non-randomized test. Randomization is used to extend any exact test relating to meansof variables with finitely many outcomes to variables with outcomes belonging to agiven bounded set. Tests in terms of variance and covariance are reduced to testsrelating to means. Randomness is then eliminated in a separate step.This method is used to create confidence intervals for the difference between twomeans (or variances) and tests of stochastic inequality and correlation.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.

Small-area estimation with spatial similarity

A class of composite estimators of small area quantities that exploit spatial (distancerelated)similarity is derived. It is based on a distribution-free model for the areas, but theestimators are aimed to have optimal design-based properties. Composition is applied alsoto estimate some of the global parameters on which the small area estimators depend.It is shown that the commonly adopted assumption of random effects is not necessaryfor exploiting the similarity of the districts (borrowing strength across the districts). Themethods are applied in the estimation of the mean household sizes and the proportions ofsingle-member households in the counties (comarcas) of Catalonia. The simplest version ofthe estimators is more efficient than the established alternatives, even though the extentof spatial similarity is quite modest.

Decision making in uncertain and changing environments

We consider an agent who has to repeatedly make choices in an uncertainand changing environment, who has full information of the past, who discountsfuture payoffs, but who has no prior. We provide a learning algorithm thatperforms almost as well as the best of a given finite number of experts orbenchmark strategies and does so at any point in time, provided the agentis sufficiently patient. The key is to find the appropriate degree of forgettingdistant past. Standard learning algorithms that treat recent and distant pastequally do not have the sequential epsilon optimality property.

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics known from map analysis in geographic information systems.Assigning phases independently to objects in RD is modelled by a single-trial multinomialrandom function Z(x), where the probabilities of phases add to one and areexplicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistenciesof the tests based on the conventional joins{count statistics and their possiblycontradictory interpretations are avoided. In practical applications we assume that theprobabilities of phases do not depend on the location but are identical everywhere inthe domain of de nition. Thus, the model involves the sum of r independent identicalmultinomial distributed 1-trial random variables which is an r-trial multinomialdistributed random variable. The probabilities of the distribution of the r counts canbe considered as a composition in the Q-part simplex SQ. They span the so calledHardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This isa generalisation of the well-known Hardy-Weinberg law of genetics. If the assignmentof phases accounts for some kind of spatial dependence, then the r-trial probabilitiesdo not remain on H. This suggests the use of the Aitchison distance between observedprobabilities to H to test dependence. Moreover, when there is a spatial uctuation ofthe multinomial probabilities, the observed r-trial probabilities move on H. This shiftcan be used as to check for these uctuations. A practical procedure and an algorithmto perform the test have been developed. Some cases applied to simulated and realdata are presented.Key words: Spatial distribution of crystals in rocks, spatial distribution of phases,joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinbergmanifold, Aitchison geometry

Formation and distribution of point defects on a disclination line near a free nematic interface

Point defects of opposite signs can alternately nucleate on the -1/2 disclination line that forms near the free surface of a confined nematic liquid crystal. We show the existence of metastable configurations consisting of periodic repetitions of such defects. These configurations are characterized by a minimal interdefect spacing that is seen to depend on sample thickness and on an applied electric field. The time evolution of the defect distribution suggests that the defects attract at small distances and repel at large distances.

The Spread of free-riding behavior in a social network

We study a model where agents, located in a social network, decide whether to exert effort or not in experimenting with a new technology (or acquiring a new skill, innovating, etc.). We assume that agents have strong incentives to free ride on their neighbors' effort decisions. In the static version of the model efforts are chosen simultaneously. In equilibrium, agents exerting effort are never connected with each other and all other agents are connected with at least one agent exerting effort. We propose a mean-field dynamics in which agents choose in each period the best response to the last period's decisions of their neighbors. We characterize the equilibrium of such a dynamics and show how the pattern of free riders in the network depends on properties of the connectivity distribution.

Measuring intergenerational earnings mobility in Spain: a selection-bias-free approach

This paper analyses intergenerational earnings mobility in Spain correcting for different selection biases. We address the co-residence selection problem by combining information from two samples and using the two-sample two-stage least square estimator. We find a small decrease in elasticity when we move to younger cohorts. Furthermore, we find a higher correlation in the case of daughters than in the case of sons; however, when we consider the employment selection in the case of daughters, by adopting a Heckman-type correction method, the diference between sons and daughters disappears. By decomposing the sources of earnings elasticity across generations, we find that the correlation between child's and father's occupation is the most important component. Finally, quantile regressions estimates show that the influence of the father's earnings is greater when we move to the lower tail of the offspring's earnings distribution, especially in the case of daughters' earnings.

Emissions distribution in post-Kyoto international negotiations: a policy

An abundant scientific literature about climate change economics points out that the future participation of developing countries in international environmental policies will depend on their amount of pay offs inside and outside specific agreements. These studies are aimed at analyzing coalitions stability typically through a game theoretical approach. Though these contributions represent a corner stone in the research field investigating future plausible international coalitions and the reasons behind the difficulties incurred over time to implement emissions stabilizing actions, they cannot disentangle satisfactorily the role that equality play in inducing poor regions to tackle global warming. If we focus on the Stern Review findings stressing that climate change will generate heavy damages and policy actions will be costly in a finite time horizon, we understand why there is a great incentive to free ride in order to exploit benefits from emissions reduction efforts of others. The reluctance of poor countries in joining international agreements is mainly supported by historical responsibility of rich regions in generating atmospheric carbon concentration, whereas rich countries claim that emissions stabilizing policies will be effective only when developing countries will join them.Scholars recently outline that a perceived fairness in the distribution of emissions would facilitate a wide spread participation in international agreements. In this paper we overview the literature about distributional aspects of emissions by focusing on those contributions investigating past trends of emissions distribution through empirical data and future trajectories through simulations obtained by integrated assessment models. We will explain methodologies used to elaborate data and the link between real data and those coming from simulations. Results from this strand of research will be interpreted in order to discuss future negotiations for post Kyoto agreements that will be the focus of the next. Conference of the Parties in Copenhagen at the end of 2009. A particular attention will be devoted to the role that technological change will play in affecting the distribution of emissions over time and to how spillovers and experience diffusion could influence equality issues and future outcomes of policy negotiations.

Cognition, Resources, and Institutions in the Explanation of Attitudes to Free Trade

This article proposes a framework for the analysis of attitudes to foreign trade policies that challenges the traditional skill-endowment approach. The traditional approach assumes informed individuals who calculate the costs and benefits of alternative policies. We propose that individuals lack information and that their positions rest on economic vulnerability, as mediated through risk-aversion. We also stress the role of environmental signals and political endorsements in guiding individuals' views on trade policy. We test this alternative approach with a Spanish survey conducted in May 2009 and the ISSP survey conducted in 2003 in a large number of less developed and more developed countries. The Spanish data show that the population is largely uninformed and that their ideas about the consequences of free trade policy do not explain attitudes among different socio-demographic groups. Meanwhile, the ISSP data contradict important aspects of the traditional approach and are consistent with the alternative approach.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

On the automatic application of inequality indexes in the analysis of the international distribution of environmental indicators

In recent years traditional inequality measures have been used to quite a considerable extent to examine the international distribution of environmental indicators. One of its main characteristics is that each one assigns different weights to the changes that occur in the different sections of the variable distribution and, consequently, the results they yield can potentially be very different. Hence, we suggest the appropriateness of using a range of well-recommended measures to achieve more robust results. We also provide an empirical test for the comparative behaviour of several suitable inequality measures and environmental indicators. Our findings support the hypothesis that in some cases there are differences among measures in both the sign of the evolution and its size. JEL codes: D39; Q43; Q56. Keywords: international environment factor distribution; Kaya factors; Inequality measurement

Free Technology Academy : a Joint Venture of Free Software and OER

The decision to publish educational materials openly and under free licenses brings up the challenge of doing it in a sustainable way. Some lessons can be learned from the business models for production, maintenance and distribution of Free and Open Source Software. The Free Technology Academy (FTA) has taken on these challenges and has implemented some of these models. We briefly review the FTA educational programme, methodologies and organisation, and see to which extent these models are proving successful in the case of the FTA.