In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an...

The shorth plot is a tool to investigate probability mass concentration. It is a graphical representation of the length of the shorth, the shortest interval covering a certain fraction of the distribution, localized by forcing the intervals considered to contain a given point x. It is easy to...

This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a...

An elliptical copula model is a distribution function whose copula is that of an elliptical distribution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be...

This paper provides a survey of three families of flexible parametric probability density functions (the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sine distributions) which can be used in modeling a wide variety of econometric problems....

This paper discusses three families of flexible parametric probability density functions: the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sin distributions. These families allow quite flexible modeling the first four moments of a...

In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly multivariate setting. We consider a...

This paper proposes a methodology to incorporate bivariate models in numerical computations of counterfactual distributions. The proposal is to extend the works of Machado and Mata (2005) and Melly (2005) using the grid method to generate pairs of random variables. This contribution allows...

In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an...