Simultaneous tests for equality of latent roots against certain alternatives-II

Krishnaiah, P. R.; Waikar, V. B.

doi:10.1007/bf02479739

Cited by 24 publications

(4 citation statements)

References 7 publications

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“…of κ 2 E (A). We point out that the key derivation steps developed in this section may also be useful for characterizing the distributional properties of more general condition number metrics, given in [27,28,29].…”

Section: Asymptotic Characterization Of κmentioning

confidence: 99%

“…al. in a sequence of papers [27,28,29] to derive the inferences on certain sub-hypotheses when the total hypothesis, which is composed of various component sub-hypotheses, is rejected. Recently, it was shown in [6] that the condition number of the form (1.2) is useful in analyzing the loss of precision in the computation of the solution to the classical linear least squares problem.…”

mentioning

confidence: 99%

“…al. [27,28,29] in certain hypothesis testing problems. Therein, they employed a result due to Davis [15], which gives an expression for the p.d.f.…”

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confidence: 99%

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Distributions of Demmel and Related Condition Numbers

Dharmawansa¹,

McKay²,

Chen³

2013

SIAM J. Matrix Anal. & Appl.

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Consider a random matrix A ∈ C m×n (m ≥ n) containing independent complex Gaussian entries with zero mean and unit variance, and let 0 < λ 1 ≤ λ 2 ≤ · · · ≤ λn < ∞ denote the eigenvalues of A * A, where (·) * represents conjugate-transpose. This paper investigates the distribution of the random variables n j=1 λ j λ k for k = 1 and k = 2. These two variables are related to certain condition number metrics, including the so-called Demmel condition number, which have been shown to arise in a variety of applications. For both cases, we derive new exact expressions for the probability densities and establish the asymptotic behavior as the matrix dimensions grow large. In particular, it is shown that as n and m tend to infinity with their difference fixed, both densities scale on the order of n 3 . After suitable transformations, we establish exact expressions for the asymptotic densities, obtaining simple closed-form expressions in some cases. Our results generalize the work of Edelman on the Demmel condition number for the case m = n.

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Section: Asymptotic Characterization Of κmentioning

confidence: 99%

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confidence: 99%

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Distributions of Demmel and Related Condition Numbers

Dharmawansa¹,

McKay²,

Chen³

2013

SIAM J. Matrix Anal. & Appl.

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“…Procedures for testing H against A5 and the associated distribution problems are discussed in a companion paper [12].…”

Section: Tests For Equality Of Latent Rootsmentioning

confidence: 99%