High-Dimensional Mahalanobis Distances of Complex Random Vectors

• In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c = p/n -> infinity. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F = S2-1S1-the product of a sample covariance matrix S-1 (from the independent variable array (be(Z(i))(1xn)) with the inverse of another covariance matrix S-2 (from the independent variable array (Z(j not equal i))(pxn))-are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S-1 and S-2 of the F-matrix is not required.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Mahalanobis distance

complex random vector

moments of MDs

Statistik

Statistics

Statistics/Econometrics

Publikations- och innehållstyp

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