Flexible modelling in statistics: past, present and future

In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well as researchers and practitioners from domains such as economics, finance or environmental sciences. This is reflected by the wealth of existing proposals for flexible distributions; well-known examples are Azzalini's skew-normal, Tukey's $g$-and-$h$, mixture and two-piece distributions, to cite but these. My aim in the present paper is to provide an introduction to this research field, intended to be useful both for novices and professionals of the domain. After a description of the research stream itself, I will narrate the gripping history of flexible modelling, starring emblematic heroes from the past such as Edgeworth and Pearson, then depict three of the most used flexible families of distributions, and finally provide an outlook on future flexible modelling research by posing challenging open questions.Comment: 27 pages, 4 figure

A note on Ramsey and Corlett-Hague rules

Ramsey-type results dictate that an optimal pattern of taxes must tax more heavily those goods which have a more inelastic(compensated)demand. Corlett and Hague (1953) investigated the optimal revenue-neutral movements from an initial uniform tax. They obtained that the goods (relatively) more complementary to the untaxed good (leisure)should see their taxes increased-which in a revenue-neutral seeting implies that the other goods see their taxes disminished. In a three-good economy (with only two goods being subject to taxation) the Ramsey-type rule and the Corlett-Hague result can be easily related

An anger and aggression group for third and fourth grade students in a rural school setting

Master's Project (M.Ed.) University of Alaska Fairbanks, 2014Children deal with anger in many different ways when they are growing up. Many children do not realize that anger is an emotion that needs to be expressed, and it can be done so in a number of positive, constructive ways. This project that resulted in an anger and aggression group for third and fourth grade students in a rural school setting can help children understand why it is so important to understand emotions of anger and learn how to express these emotions positively. The literature suggests by assessing children at a younger age, if parents/guardians, families, counselors and other school staff can combat the issue of school age children being unable to understand their feelings of anger and aggression. Families also need to support their child and the therapist by continuing to help the child learn and grow in the home

Skew-symmetric distributions and Fisher information -- a tale of two densities

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback of a potentially singular Fisher information in the vicinity of symmetry. All existing results indicate that Gaussian densities (possibly after restriction to some linear subspace) play a special and somewhat intriguing role in that context. We dispel that widespread opinion by providing a full characterization, in a general multivariate context, of the information singularity phenomenon, highlighting its relation to a possible link between symmetric kernels and skewing functions -- a link that can be interpreted as the mismatch of two densities.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ346 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the Private Provision of Public Goods: A Diagrammatic Exposition

This paper surveys a selection of the literature on the private provision of public goods using the Kolm triangle. (The Kolm triangle is the analogue of an Edgeworth box in an economy with a public good.) We provide simple geometrical proofs of various established results using this graphical device. Our reference framework is the model of private contributions to public goods developed by Bergstrom, Blume and Varian (1986). With the Kolm triangle, we can easily study the existence and uniqueness of Nash equilibria, the effects of redistribution of the initial wealth, the level of provision in Stackelberg equilibria, the effects of subsidizing private contributions, and the implementation of Lindahl equilibria.Public Goods, Nash Equilibrium, Stackelberg Equilibrium, Lindahl Equilibrium, Kolm triangle, Redistribution, Subsidies, Regressive Redistribution of Income

A tractable, parsimonious and flexible model for cylindrical data, with applications

In this paper, we propose cylindrical distributions obtained by combining the sine-skewed von Mises distribution (circular part) with the Weibull distribution (linear part). This new model, the WeiSSVM, enjoys numerous advantages: simple normalizing constant and hence very tractable density, parameter-parsimony and interpretability, good circular-linear dependence structure, easy random number generation thanks to known marginal/conditional distributions, flexibility illustrated via excellent fitting abilities, and a straightforward extension to the case of directional-linear data. Inferential issues, such as independence testing, circular-linear respectively linear-circular regression, can easily be tackled with our model, which we apply on two real data sets. We conclude the paper by discussing future applications of our model.Comment: 17 pages, 5 figure

Switching regressions and activity analysis.

We study the use of switching regression models to characterize the coefficients in linear production technologies with a finite number of activities. Maximum likelihood-based methods are proposed and different switching specifications are discussed. The viability of these newly proposed technniques is established. The methods developed combine the advantages of the two major approaches to frontier estimation: the functional flexibility of the linear programing-nonparametric and nonstatistical-approach and the statistical nature of the econometric-both parametric and statistical-approach. This combination comes at the expense of some analytical complexity.Switching regression models; Activity analysis; Linear production models;

Optimal Provision of Public Goods with Altruistic Individuals

We study the optimal provision of public goods in the context of a special class of altruistically linked utility functions. We show that the usual Samuelson condition holds as if the utility functions were independent.Samuelson condition, Pareto efficiency

A note on Ramsey and Corlett-Hague rules.

Ramsey-type results dictate that an optimal pattern of taxes must tax more heavily those goods which have a more inelastic(compensated)demand. Corlett and Hague (1953) investigated the optimal revenue-neutral movements from an initial uniform tax. They obtained that the goods (relatively) more complementary to the untaxed good (leisure)should see their taxes increased-which in a revenue-neutral seeting implies that the other goods see their taxes disminished. In a three-good economy (with only two goods being subject to taxation) the Ramsey-type rule and the Corlett-Hague result can be easily related.Optimal taxation; Ramsey; Corlett-Hague; Demand elasticity;