EXISTENCE, UNIQUENESS AND SOME COMPARATIVE STATICS FOR RATIO- AND LINDAHL EQUILIBRIA: NEW WINE IN OLD BOTTLES

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost-share or ratio equilibrium. Finally, we indicate how it may be ex-ploited to facilitate comparative static analysis of Lindahl and cost share equilibria.Public goods, Lindahl equilibrium, ratio equilibrium.

Existence, Uniqueness and Some Comparative Statics for Ratio- and Lindahl Equilibria: New Wine in Old Bottles

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost-share or ratio equilibrium. Finally, we indicate how it may be ex-ploited to facilitate comparative static analysis of Lindahl and cost share equilibria.public goods, Lindahl equilibrium, ratio equilibrium

Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

Invariant Models for Causal Transfer Learning

Methods of transfer learning try to combine knowledge from several related tasks (or domains) to improve performance on a test task. Inspired by causal methodology, we relax the usual covariate shift assumption and assume that it holds true for a subset of predictor variables: the conditional distribution of the target variable given this subset of predictors is invariant over all tasks. We show how this assumption can be motivated from ideas in the field of causality. We focus on the problem of Domain Generalization, in which no examples from the test task are observed. We prove that in an adversarial setting using this subset for prediction is optimal in Domain Generalization; we further provide examples, in which the tasks are sufficiently diverse and the estimator therefore outperforms pooling the data, even on average. If examples from the test task are available, we also provide a method to transfer knowledge from the training tasks and exploit all available features for prediction. However, we provide no guarantees for this method. We introduce a practical method which allows for automatic inference of the above subset and provide corresponding code. We present results on synthetic data sets and a gene deletion data set

Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.Comment: 42 page

Cultural Priming and Psychosocial Factors in the Achievement of Hispanic and White Students

The rationale for this study is that the achievement gap between Whites and Hispanics can be influenced by reconceptualizing the learner process as one that integrates culture, motivation, and psychosocial variables, with academic performance. The study investigated the role of three psychosocial variables in achievement: familism, academic self concept, and ethnocentrism. It also reconceptualized one’s culture as a toolkit for instrumental use on tasks in another culture, adopted the dynamic constructivist approach to culture’s influence, and applied the original definition of acculturation, of mutual influence of groups in contact, to achievement. A pretest/posttest comparison group design was used. White and Hispanic 8th grade students (N=72) met for two sessions. Students took pretests of the psychosocial variables, background variables related to ethnicity, and math. One month later, students were randomly assigned to the Hispanic, American, or Neutral priming conditions, given the priming task, an indirect test on psychosocial variables, the posttests of the psychosocial variables, and math. Results supported hypotheses that psychosocial variables moderate the impact of culture on achievement. Cultural priming significantly influenced psychosocial variables (effect sizes from 9-22%). Psychosocial variables significantly influenced math achievement (effect sizes from 8-17%; they significantly predicted math achievement (adjusted R square 13-22%); and they moderated culture’s impact on achievement (adjusted R square 17.8%). Findings support a two-step learner process of culture affecting psychosocial variables, which, in turn, affect academic achievement. Academic self-concept had a positive effect, ethnocentrism, a negative one, but its interaction effects with priming were positive. Familism was not a significant factor. Results did not support hypotheses based on group differences in, or correlations between, psychosocial variables based on group stereotypes, suggesting culture’s impact on achievement is more related to learner processes. Combinations of levels of academic self-concept and ethnocentrism were associated with group differences in achievement. Hispanic primes affected Whites, and American primes, Hispanics, providing support for the interdependence of achievement. The study is significant in showing culture’s influence on achievement comes through affect and motivation. Implications include a new understanding of culture’s impact on achievement, the relevance of minority culture to learning, and potential individualization of instruction within ethnic groups