Negative binomial and Poisson processes {X(t), t ≥ 0} have cumulants proportional to the rate λ. So, formal Cornish-Fisher expansions in powers of λ−1/2 are available for their cumulative distribution function and quantiles. If T is an independent random variable with cumulants proportional to γ then the cumulants of X(T ) are proportional to γ; so, CornishFisher expansions in powers of γ−1/2 a...

Quantiles, also known as value-at-risks in the financial industry, are important measures of random performances. Quantile sensitivities provide information on how changes in input parameters affect output quantiles. They are very useful in risk management. In this article, we study the estimation of quantile sensitivities using stochastic simulation. We propose a kernel estimator and prove tha...

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distri...

Suppose data consist of a random sample from a distribution function FY , which is unknown, and that interest focuses on inferences on θ, a vector of quantiles of FY . When the likelihood function is not fully specified, a posterior density cannot be calculated and Bayesian inference is difficult. This article considers an approach which relies on a substitution likelihood characterized by a ve...

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of differ...

We derive the Edgeworth expansion for the studentized version of the kernel quantile estimator. Inverting the expansion allows us to get very accurate confidence intervals for the pth quantile under general conditions. The results are applicable in practice to improve inference for quantiles when sample sizes are moderate.

Modern applications require processing streams of data for estimating statistical quantities such as quantiles with small amount of memory. In many such applications, in fact, one needs to compute such statistical quantities for each of a large number of groups (e.g.,network traffic grouped by source IP address), which additionally restricts the amount of memory available for the stream for any...

Abstract. The paper considers recent approaches to testing homogeneity in a finite mixture model, the modified likelihood ratio test (MLRT) of Chen et al. (2001) and the D-tests of Charnigo and Sun (2004). They are adapted to Weibull mixtures with and without a Weibull-to-exponential transformation of the data. Critical quantiles are calculated by simulation. To cope with the dependency of quan...

For extreme events, estimation of high conditional quantiles for heavy tailed distributions is an important problem. Quantile regression is a useful method in this field with many applications. Quantile regression uses an L1-loss function, and an optimal solution by means of linear programming. In this paper, we propose a weighted quantile regression method. Monte Carlo simulations are performe...

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 convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0, 1]. We derive the almost sure convergence and the asymptotic normality for these estimators. Th...