490 research outputs found
Goodness-of-fit tests in many dimensions
A method is presented to construct goodness-of-fit statistics in many
dimensions for which the distribution of all possible test results in the limit
of an infinite number of data becomes Gaussian if also the number of dimensions
becomes infinite. Furthermore, an explicit example is presented, for which this
distribution as good as only depends on the expectation value and the variance
of the statistic for any dimension larger than one.Comment: 14 page
Scaling limits for the Lego discrepancy
For the Lego discrepancy with M bins, which is equivalent with a
chi^2-statistic with M bins, we present a procedure to calculate the moment
generating function of the probability distribution perturbatively if M and N,
the number of uniformly and randomly distributed data points, become large.
Furthermore, we present a phase diagram for various limits of the probability
distribution in terms of the standardized variable if M and N become infinite.Comment: 16 page
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