论文信息 - Inefficiency and correlation

Inefficiency and correlation

SUMMARY Various extremal results have been proved concerning the efficiency of least squares estimates relative to Gauss-Markov estimates and concerning the canonical correlations between two sets of random variables. In this paper we show how these two types of result are related, and derive a new result from which many previous inequalities can be derived. Some key word8: Canonical correlation; Inefficiency; Least squares. The inequality for the generalized efficiency of least squares estimates relative to best linear unbiased estimates (Bloomfield & Watson, 1975; Knott, 1975) has found applications in other areas. A consequence was used by Venables (1976) in testing for sphericity of a Gaussian distribution, and by Khatri (1978) in proving extremal results for canonical correlations. We shall prove a slightly more general result concerning canonical

Peter Bloomfield | P. Bloomfield | Flavio C. Bartmann | F. Bartmann

[1] G. S. Watson. Prediction and the efficiency of least squares , 1972 .

[2] Geoffrey S. Watson,et al. Linear Least Squares Regression , 1967 .

[3] M. Knott,et al. On the minimum efficiency of least squares , 1975 .

[4] Geoffrey S. Watson,et al. The inefficiency of least squares , 1975 .

[5] S. Haberman. How Much Do Gauss-Markov and Least Square Estimates Differ? A Coordinate-Free Approach , 1975 .

[6] C. Khatri. Some optimization problems with applications to canonical correlations and sphericity tests , 1978 .

[7] R. Bargmann,et al. Maximum eccentricity as a union-intersection test statistic in multivariate analysis , 1978 .

[8] Calyampudi Radhakrishna Rao,et al. Linear Statistical Inference and its Applications , 1967 .

[9] W. Venables. Some implications of the union-intersection principle for tests of sphericity , 1976 .