This paper describes a randomization-based estimation and inference procedure for the distribution or quantiles of potential outcomes with a binary treatment and instrument. The method imposes no parametric model for the treatment effect, and remains valid for small n, a weak instrument, or inference on tail quantiles, when conventional large-sample methods break down. The method is illustrated...

Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value at risk. The variance of the weighted 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 ofweighted empirical distributions. Under regular...

Title of dissertation: SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES Lemeng Pan, Doctor of Philosophy, 2016 Dissertation directed by: Professor Benjamin Kedem Department of Mathematics In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, na...

A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the distribution of the total cost accumulated in a run. This includes the probability of large total costs, the median cost, and other quantiles. While expectations...

This paper proposes a technique for estimating steady-state quantiles from discrete-event simulation models, with particular attention paid to cycle-time quantiles of manufacturing systems. The technique is justified through an extensive empirical study and supported with mathematical analysis. The Cornish-Fisher expansion is used as a basis for this estimation, and it is shown that for an M/M/...

Analogues of linear-combinations-of-order-statistics, or L-estimators, are suggested for estimating the parameters of the linear regression model. The methods are based on linear combinations of the p-dimensional "regression quantiles" proposed by Koenker and Bassett. A uniform Bahadur-type representation of regression quantiles is established, and this permits a general theory of L-estimators ...

The quantile approximation method has recently been proposed as a simple method for deriving confidence intervals for the treatment effect in a random effects meta-analysis. Although easily implemented, the quantiles used to construct intervals are derived from a single simulation study. Here it is shown that altering the study parameters, and in particular introducing changes to the distributi...

Abstract: QQ-plots are extremely useful in univariate data analysis. In this article, Koltchinskii (1997) and Chaudhuri’s (1996) definition of multivariate quantile is used to develop analogous plots for bivariate data. Bivariate qq-plots are exhibited for comparing a sample to a given population distribution (the bivariate normal), and for comparing two or more bivariate samples. The plots are...

The principle of self-consistency has been employed to estimate regression quantile with randomly censored response. It has been of great interest to study how the self-consistent estimation of censored regression quantiles is connected to the alternative martingale-based approach. In this talk, I will first present a new formulation of self-consistent censored regression quantiles based on sto...

In this paper, we propose a multivariate quantile regression method which enables localized analysis on conditional quantiles and global comovement analysis on conditional ranges for high-dimensional data. The proposed method, hereafter referred to as FActorisable Sparse Tail Event Curves, or FASTEC for short, exploits the potential factor structure of multivariate conditional quantiles through...