Nonparametric testing for a monotone hazard function: making a global test
local
  Nancy Heckman
  Statistics Department
  University of British Columbia 


There are several well-known tests of the null hypothesis that the hazard 
function is non-increasing. However, these tests were designed to have power 
against the alternative that the hazard function is always increasing. They
do 
not have much power when, say, the hazard is increasing on only a small 
interval. Fortunately we can modify these tests so that they can detect an 
increase on a small interval. Specifically, the test of Proschan and Pyke 
(1967), based on normalized spacings, is modified to a more local test. The 
significance level of the local test is attained when the data are
exponentially 
distributed, and thus we can easily calculate p-values via simulation. The
idea 
of localizing the Proschan and Pyke test is inspired by recent developments
in 
nonparametric inference in bump-hunting in regression analysis.



This is joint work with Irene Gijbels