Multivariate Estimation from "Two Variables at a Time" Observations

Abstract

Suppose that we wish to estimate the mean µ and the covariance Cof a random p-vector X with p > 2, but we can only sample from thevector X two of its p components at a time. We give both nonparametric estimates and the maximum likelihood estimates (MLEs) undernormality, and their covariances.

Keywords

• Maximum likelihood estimation,Multivariate normal,Nonparametric estimation,2000 AMS Classification: 62F10

References

1. Anderson, T. W., An Introduction to Multivariate Statistical Analysis, third edition. John Wiley and Sons, New York, 2003.
2. Cleveland, W. S., Robust locally weighted regression and smoothing scatterplots, Journal of the American Statistical Association, 74, 829-836, 1979.
3. Cleveland, W. S., LOWESS: A program for smoothing scatterplots by robust locally weighted regression, The American Statistician, 35, 54, 1981.
4. Davidovitz, M., Reconstruction of the S-matrix for a 3-port using measurements at only two ports, IEEE Microwave and Guided Wave Letters, 5, 349-350, 1995. McNabb, D. E., Research Methods for Political Science: Quantitative and Qualitative Methods, M. E. Sharpe Publishers, London, 2004.
5. Premoli, A. and Storace, M.,Two-port ideal power transferitors: a unified introduction to ideal transformer and gyrator, IEEE Transactions on Circuits and Systems II: Express Briefs, 51, 426-429, 2004.
6. Withers, C. S., Nonparametric confidence intervals for functions of several distributions, Annals of the Institute of Statistical Mathematics, 40, 727-746, 1988.
7. Zhao, Y., Yu, S. and Yang, Z., Evolutionary mechanism of port clusters based on the theory of dissipative structure, In: Proceedings of the 2008 International Conference on Intelligent Computation Technology and Automation, volume 1, pp. 52-55, 2008.