Second-order accurate inference on eigenvalues of covariance and correlation matrices
Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported.
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Volume (Year): 96 (2005)
Issue (Month): 1 (September)
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References listed on IDEAS
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- Robert J. Boik, 2002. "Spectral models for covariance matrices," Biometrika, Biometrika Trust, vol. 89(1), pages 159-182, March.
- Thomas J. DiCiccio, 2002. "Accurate confidence limits for scalar functions of vector M-estimands," Biometrika, Biometrika Trust, vol. 89(2), pages 437-450, June.
- Fujikoshi, Y., 1978. "Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 63-72, March.
- Booth, J. G. & Hall, P. & Wood, A. T. A., 1994. "On the Validity of Edgeworth and Saddlepoint Approximations," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 121-138, October.
- Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
- Robert J. Boik, 2003. "Principal component models for correlation matrices," Biometrika, Biometrika Trust, vol. 90(3), pages 679-701, September.
- Boik, Robert J., 1998. "A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 244-276, November.
- Wang, Suojin, 1992. "General saddlepoint approximations in the bootstrap," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 61-66, January.
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