We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Basset [1978] can be easily extended to obtain an analogous definition for the θth sample quantity quantile instead of the usual one. By means of this definition we introduce a linear regression model for quantity quantiles and analyze some properties of the residuals. In s...

One major question in molecular biology is whether the spatial distribution of observed molecules is random or organized in clusters. Indeed, this analysis gives information about molecules' interactions and physical interplay with their environment. The standard tool for analyzing molecules' distribution statistically is the Ripley's K function, which tests spatial randomness through the compu...

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance ...

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett’s traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version, those quantiles can be computed efficiently via linear programming techniques. Consistency, Bahadur representation and asymptotic normality results are establ...

Confidence intervals for the median of estimators or other quantiles were proposed as a substitute for usual confidence intervals in terminating and steady-state simulation. They are easy to obtain, the variance of the estimator is not used, they are well suited for correlated simulation output data, apply to functions of estimators, and in simulation they seem to be particularly accurate. For ...

The Robbins-Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins-Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure...

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when an outlier takes an arbitrarily large value, and derive the breakdown points for those bootstrap quantiles. The breakdown properties characterize the situation where the implie...

Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value-at-risk. The variance of the weight sample quantile estimator is usually a difficult quantity to compute. In this paper, we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles of weighted empirical distributions. Under regular...

Intermediate quantiles play an important role in the statistics of extremes with particular applications in risk management. For interval estimation of quantiles, Chen and Hall (1993) proposed the so-called smoothed empirical likelihood method. In this paper, we apply the method in Chen and Hall (1993) to construct confidence intervals for an intermediate quantile and show that the choice of th...

Value at Risk measures the worst loss to be expected of a portfolio over a given time horizon at a given confidence level. Calculation of VaR frequently involves estimating the volatility of return processes and quantiles of standardized returns. In this paper, several semiparametric techniques are introduced to estimate the volatilities . In addition, both parametric and nonparametric techniqu...