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A Comparison of Methods for Approximating the Mean Eigenvalues of a Random Matrix

Abstract This paper proposes several methods for approximating the expected value of an eigenvalue of a random matrix. A comparative study assesses the accuracy of these methods. The proposed methods for approximating the mean value of an eigenvalue of a random matrix consist of a regression approach using the dimensions of the data and position of the eigenvalue as predictors, two methods using expected values of order statistics for the normal distribution, and another approach using percentiles of the normal distribution. These methods provide researchers who desire to readily determine the dimensionality of data by using parallel analysis, with easy-to-implement alternatives to calculate the mean eigenvalues of a random matrix.