Nonparametric Estimation of a Distribution with Type I Bias

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Hammou ElBarmi*+ and Alessandra Alfieri
• Affiliation(s): Kansas State University and United Nations
• Keywords: Nonparametric estimation ; Type I bias ; Competing risks ; Hypotheses testing ; Weak convergence

Abstract

A random variable $X$ is said to have a symmetric distribution about $a$ if $X-a$ and $-X+a$ are identically distributed. By considering various types of partial orderings between the distributions of $X-a$ and $-X+a$ one obtains various types of partial skewness or one sided bias. For example, $F$ is said to have type I bias about $a$ if $\overline{F} (a+x) \ge F((a-x)-)$ for all $x \ge 0$. In this talk, we assume that $a=0$ and propose a non-parametric estimator of $F$ under the restriction that $F$ has a type I bias and study its weak convergence. We also provide a test for symmetry against type I bias. The results of a simulation study show that the proposed estimator outperforms in terms of mean square error the NPMLE at all the quantiles of the distributions considered. We show how the results obtained could be used to compare two competing risks in a competing risks model and illustrate the results with a real life example.