Minimum Quantile Distance Estimation of Quantiles Using Linear Combinations of Standard Quantile Functions as Models

• Activity Number: 538
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Dean H. Fearn *+ and Elliott Nebenzahl
• Companies: California State University, East Bay and California State University, East Bay
• Keywords: quantile estimation ; minimum distance ; linear model ; maximum likelihood

Abstract

We select the constant quantile function along with at least one other well known standard quantile function(s) and then select the coefficients corresponding to these functions that minimize the distance between the ensuing linear combination and the sample quantile function. This linear combination is thus assured to be close to the sample quantile function. We use this linear combination approach to make inferences (estimation and/or hypothesis testing and/or confidence intervals) about pth quantiles of the true distribution for small p. We compare our technique of estimating these quantiles to classical methods, such as maximum likelihood, and show that our technique is more robust, in that the technique introduced by us tends to be more accurate over a wider class of possible true distributions.