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

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

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

On Plutocratic and Democratic CPIs

Prais (1958) showed that the standard CPI computed by most statistical agencies can be interpreted as a plutocratic weighted average of household price indexes because the weight of each household in the official CPI is determined by its total expenditures. In this paper, we decompose the difference between the standard CPI and a democratically weighted index as the product of a measure of income inequality and the sample covariance between the elementary individual price indexes and a parameter which is a function of the income elasticity of each good.

Analysis of biological and biomedical data with circular statistics

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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

Efficient inference about the tail weight in multivariate Student tt distributions

We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root-$n$ consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.Comment: 23 page

Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of the MLE and its limiting normal distribution. Our approach to this fundamental issue is based on a sound combination of the Delta method, Stein's method, Taylor expansions and conditional expectations, for the classical situations where the MLE can be expressed as a function of a sum of independent and identically distributed terms. This encompasses in particular the broad exponential family of distributions.Comment: 15 pages, 1 tabl

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

Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We use these bounds to study the asymptotic behavior of weakly coupled systems of fully nonlinear parabolic equations. Our results apply to some "asymmetric systems" where some equations contain a sublinear Hamiltonian whereas the others contain a superlinear one. Moreover, we can deal with some particular case of systems containing some degenerate equations using a generalization of the strong maximum principle for systems