Independence Empirical Processes
Let H be a probability measure on the measurable space (X x y, A x B) with marginal laws P and Q on (X, A) and (y, B), respectively. Given a sample (X 1, Y 1),..., (X n , Y n ) of independently and identically distributed vectors from H, we want to test the null hypothesis of independence H o : H = P x Q versus the alternative hypothesis H 1: H ≠ P x Q. Let H n be the empirical measure of the observations, and let P n , and Q n be its marginals. The latter are the empirical measures of the X i ’s and Yx’s, respectively.
KeywordsNull Hypothesis Covariance Function Gaussian Process Empirical Measure Original Observation
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