Abstract
This paper derives the likelihood ratio statistic to test the nullity of the multiple correlation coefficient between X 1 and (X 2,...,X k ) under the assumption that (X1, X2,..., Xk) has a multivariate normal distribution and a sample of size n is available, where for N observation vectors all components are available, while for M = (n - N) observation vectors, the data on the last q components, (X k-q+1,X k-q+2,...,X k), are missing.
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References
Afifi, A. A., and R. M. Elashoff (1966), “Missing observations in multivariate statistics I. Review of the literature.”Journal of the American Statistical Association 61, 595–604.
Afifi, A. A., and R. M. Elashoff (1967), “Missing observations in multivariate statistics II. Point estimation in simple linear regression.”Journal of the American Statistical Association62, 10–29.
Afifi, A. A., and R. M. Elashoff (1969a), “Missing observations in multivariate statistics III: Large sample analysis of simple linear regression.”Journal of the American Statistical Association64, 337–358.
Afifi, A. A., and R. M. Elashoff (1969b), “Missing observations in multivariate statistics—IV. A note on simple linear regression.”Journal of the American Statistical Association64, 359–365.
Anderson, T. W. (1957), “Maximum likelihood estimates for a multivariate normal distribution when some observations are missing.”Journal of the American Statistical Association52, 200–203.
Anderson, T. W. (1958),An Introduction to Multivariate Analysis. New York: Wiley.
Bhargava, R. P. (1975), “Someone-sample hypothesis testing problems when there is a monotone sample from a multivariate normal population.”Annals of the Institute of Statistical Mathematics27, 327–339.
Giri, N. (1977),Multivariate Statistical Inference. New York: Academic Press.
Eaton, M. L., and T. Kariya (1974), “Testing for independence with additional information.” Technical Report No. 238. University of Minnesota.
Eaton, M. L., and T. Kariya (1975), “Tests on means with additional information.” Technical Report No. 243. University of Minnesota.
Edgett, G. L. (1956), “Multiple regression with missing observations among the independent variables.”Journal of the American Statistical Association51, 122–131.
Little, R. J. A. (1976), “Inference about means from incomplete multivariate data.”Biometrika63, 593–604.
Lord, F. M. (1955), “Estimation of parameters from incomplete data.”Journal of the American Statistical Association 50, 870–876.
Morrison, D. F. (1971), “Expectations and variances of maximum likelihood estimates of the multivariate normal distribution parameters with missing data.”Journal of the American Statistical Association 66, 602–604.
Radhakrishnan, R. (1982), “Inadmissibility of the maximum likelihood estimator for a multivariate normal distribution when some observations are missing.”Communications in Statistics A, Theory and Methods11, 941–955.
Rao, C. R. (1956), “Analysis of dispersion with incomplete observations on one of the characters.”Journal of the Royal Statistical Society, Series B19, 259–264.
Smith, W. B., and R. C. Pfaffenberger (1970), “Selection index estimation from partial multivariate normal data.”Biometrics 26, 625–639.
Trawinski, I. M., and R. E. Bargmann (1964), “Maximum likelihood estimation with incomplete multivariate data.”Annals of Mathematical Statistics35, 647–657.
Wilks, S. S. (1932), “Moments and distributions of estimates of population parameters from fragmentary samples.”Annals of Mathematical Statistics 3, 163–195.
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© 1987 D. Reidel Publishing Company
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Provost, S.B. (1987). Testing for the Nullity of the Multiple Correlation Coefficient with Incomplete Multivariate Data. In: MacNeill, I.B., Umphrey, G.J., Safiul Haq, M., Harper, W.L., Provost, S.B. (eds) Advances in the Statistical Sciences: Foundations of Statistical Inference. The University of Western Ontario Series in Philosophy of Science, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4788-7_14
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DOI: https://doi.org/10.1007/978-94-009-4788-7_14
Publisher Name: Springer, Dordrecht
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