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Unitary operators, empirical processes and goodness of fit problem in R^d

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Unitary operators form a world of their own. Empirical processes, and to parametric empirical processes, are, on the other hand, well defined, well studied and unequivocal objects, with developed asymptotic theory as they are. However, applying unitary operators to empirical processes leads to new type of processes with interesting and useful asymptotic properties.

In this way we are able to obtain asymptotically distribution free processes in R^d for testing hypothesis.

The approach extends to the case of discrete distributions, so that we now have a class of asymptotically distribution free goodness of fit tests, and not only one such test—the chi-square test.

This talk is part of the Statistics series.

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