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Distribution-Free Testing; the Khmaladze Transform

Tuesday, March 11, 2014 - 11:00
Priscilla (Cindy) Greenwood, Professor Emeritus, Dept. of Math, UBC; Associate Member, Dept. of Statistics, UBC
Statistics Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

The Khmaladze transform takes the vector of components of Pearson's chi-square statistic to another vector which contains the same "statistical information" but is asymptotically distribution-free. Hence any test statistic based on the new vector is also asymptotically distribution-free. Natural examples are goodness-of-fit statistics based on partial sums.

A version of the Khmaladze transform for testing whether data comes from a continuous distribution function, F, maps the normalized error function, which is asymptotically an F-bridge, to a process which is asymptotically a standard Brownian bridge. The associated statistic, which is empirically based, can be used for distribution-free testing.