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...

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...

Previous research has confirmed that the distribution of bids for construction auctions can be reasonably modeled with Lognormal distribution. The location parameter this (the mean μ) been found to have a good linear correlation bidders’ cost estimates. However, scale (standard deviation bids, σ) remains noticeably difficult anticipate. By analyzing 13 auction datasets, hard evidence is provide...