Brownian sheet and uniformity tests on the hypercube
Abstract
A construction of p-parameter Brownian sheet on the hypercube C=[0,1]p as a sum of 2p independent Gaussian processes is obtained. The terms are closely related to Brownian pillows, and the probability laws of their L2(C) squared norms are computed. This allows us to propose consistent tests of uniformity for samples of i.i.d. random vectors on C. A comparison of powers of the new tests with those of several uniformity tests found in the statistical literature completes the article. The proposed tests show a good performance in detecting copula alternatives. Keywords: Brownian sheet, multivariate uniformity tests.
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