Abstract #301838

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JSM 2003 Abstract #301838
Activity Number: 422
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301838
Title: Confidence Bands for Empirical Quantile Functions
Author(s): Walter A. Rosenkrantz*+
Companies: University of Massachusetts
Address: Dept. of Math & Statistics, Amherst, MA, 01003-4515,
Keywords: goodness of fit ; Kolmogorov test ; convex joint confidence set
Abstract:

Determining whether a random sample (X_1,X_2,..,X_n) comes from a given distribution F(x;b_1,b_2,..,b_n) depending on one or more unknown parameters that must be estimated from the data, is a fundamental problem in statistics, and a variety of graphical and formal methods have been proposed to study it. In a previous paper we derived simultaneous two-sided 100(1-\alpha)% confidence interval for the $p$ quantiles of a normal distribution. We use this result here to obtain a new 100(1-\alpha)% confidence band for the empirical quantile function. This extends the Kolmogorov test for the uniform distribution to the normal distribution where the distribution depends on the mean and variance, parameters that must be estimated from the data. Our method is of general character; to illustrate this, we derive a confidence band when sampling from an exponential distribution with unknown mean. Our method raises the following question of independent interest: When is the joint confidence set convex?

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