Journal
BERNOULLI
Volume 22, Issue 1, Pages 563-588Publisher
INT STATISTICAL INST
DOI: 10.3150/14-BEJ668
Keywords
Brownian bridge; empirical processes; goodness of fit tests in R-d; g-projected Brownian motions; parametric hypothesis; unitary operators
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The main message in this paper is that there are surprisingly many different Brownian bridges, some of them familiar, some of them less familiar. Many of these Brownian bridges are very close to Brownian motions. Somewhat loosely speaking, we show that all the bridges can be conveniently mapped onto each other, and hence, to one standard bridge. The paper shows that, a consequence of this, we obtain a unified theory of distribution free testing in R-d, both for discrete and continuous cases, and for simple and parametric hypothesis.
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