Part I [13] introduces the application of the barycentric approximation methodology for evaluating pro t-and-loss distributions numerically. Although, convergence of the quantiles is ensured by the weak convergence of the discrete measures, as proclaimed in [13], recent numerical results have indicated that the approximations of the pro t-and-loss distribution are less practical when the portfo...

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on linear combinations of empirical quantiles (L−statistics) of discrete variations of a sample path over a discrete grid of the interval [0, 1]. We derive the almost sure convergence for these estimators and prove the ...

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...

Stochastic simulation has become a well established paradigm used in performance evaluation of various complex dynamic systems. Most simulation output analysis is confined to the estimation of mean values. This is true for both finite horizon and steady state simulation. The estimation of quantiles provides a deeper insight into the simulated model. In this paper we describe a method for estima...

Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in...

This paper studies the performance of nonparametric quantile regression as a tool to predict Value at Risk (VaR). The approach is flexible as it requires no assumptions on the form of return distributions. A monotonized double kernel local linear estimator is applied to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, where particularly f...

We estimate the parameters of an elliptical distribution by means of a multivariate extension of the Method of Simulated Quantiles (MSQ) of Dominicy and Veredas (2010). The multivariate extension entails the challenge of the construction of a function of quantiles that is informative about the covariation parameters. The interquantile range of a projection of pairwise random variables onto the ...

We propose a multivariate extension of Yaari’s dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the ...

One of the key invariants in computer and communication systems is that im¬ portant characteristics follow long-or heavy-tailed distributions. This means that the tail of these distributions declines according to a power law. Hence, the probability for extremely large values is non-negligible. For example, such distributions have been found to describe the size of web objects or the pro¬ cessin...