Abstract
In this chapter, we aim to examine problems of testing which are based on asymptotic distributions of eigenprojections of the sample covariance matrix S n and the sample correlation matrix R n . The topic was introduced by Tyler (1981, 1983) who designed certain test statistics using the asymptotic normality of the eigenprojections of the sample covariance matrix in the case of normally and elliptically distributed populations. Some of his results were carried over to the case of the sample correlation matrix by Kollo (1984). For rotationally invariant distributions, the asymptotic properties of estimation and hypothesis testing on the basis of eigenprojections of the sample covariance matrix were discussed by Fan and Fang (1990).
The author is thankful to Professor Heinz Neudecker for inspiring discussions on matrix differentiation for many years, which have also stimulated the writing of the present paper. The author is thankful to the Estonian Research Foundation, which has supported the study through grant Nr. 3013.
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Kollo, T. (2000). Asymptotic Inference Based on Eigenprojections of Covariance and Correlation Matrices. In: Heijmans, R.D.H., Pollock, D.S.G., Satorra, A. (eds) Innovations in Multivariate Statistical Analysis. Advanced Studies in Theoretical and Applied Econometrics, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4603-0_15
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DOI: https://doi.org/10.1007/978-1-4615-4603-0_15
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