Bartlett's test for eigenvalues

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A test used in principal components analysis. The test is of the null hypothesis that the smallest m eigenvalues of a n×n variance–covariance matrix are equal to 0. Writing k=nm+1, the test statistic is , where ν is the number of degrees of freedom associated with the variance–covariance matrix, and λ1, λ2,…, λn are the eigenvalues. Under the null hypothesis, X2 has an approximate chi-squared distribution with ½(m − 1)(m − 2) degrees of freedom.

Subjects: Probability and Statistics.

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