Abstract
In elementary mathematical statistics, one studies in some detail various characteristics of the distribution of a scalar random variable. Thus its density and various parameters are considered and statements are made regarding this variable. For example, given the information above, we can compute the probability that the variable will exceed some value, say α, or that it will assume a value in the interval (α, (β) and so on.
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References
Anderson, T. W., An introduction to Multivariate Statistical Analysis, New York, Wiley, 1958. A comprehensive book devoted to multivariate analysis. The multivariate normal distribution, etc. covered here are discussed in Chapters 1, 2, 3, 4, 5, 7.
Apostol, T., Calculus, vol. 2, New York, Bladsdell, 1962. Like Courant’s volume, this is a general reference on transformations, multiple integrals, maxima-minima, etc. It has a set theoretic approach and is a more modern reference.
Bellman, R., Introduction to Matrix Analysis, New York, McGraw-Hill, 1960. A general reference for advanced topics in matrix algebra.
Courant, R., Differential and Integral Calculus, vol. 2, New York, Interscience, 1934. This volume deals with advanced calculus of several variables. Of interest are Chapters 3, 4, 8.
Hotelling, H., “ The Generalization of Student’s Ratio,” Annals of Mathematical Statistics, Vol. 2, 1931, pp. 360–378. The first paper to suggest the so-called “Hotelling T 2 statistic” to test the hypothesis (x = \i0, E unknown.
Hotelling, H., “The Most Predictable Criterion,” Journal of Educational Psychology, vol. 26, 1935, pp. 139–142.
Hotelling, H., “Relations Between Two Sets of Variates,” Biometrika, vol. 28, 1936, pp. 321–377. A follow-up on the 1935 article, using the coefficients of vector correlation and vector alienation.
Kendall, M. G., and A. Stuart, The Advanced Theory of Statistics, vol. I, New York, Hafner Publishing Co., 1958. The multivariate normal distribution is discussed in Chapter 15.
Rao, C. R., Linear Statistical Inference and Its Applications, New York, Wiley; 1965. Deals with the multivariate normal distribution etc. discussed here in Chapter 8, Sections a, b, c, d.
Wilks, S. S., Mathematical Statistics, New York, Wiley; 1962. The multivariate normal distribution is discussed in Sections 10.1, 10.2.
Wishart, J., “The Generalized Product Moment Distribution in Samples from a Normal Multivariate Population,” Biometrika, 1928, vol. 20A, pp. 32–52. The first derivation of the so-called ” Wishart’s distribution.
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© 1974 Springer-Verlag New York Inc
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Dhrymes, P.J. (1974). Elementary Aspects of Multivariate Analysis. In: Econometrics. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9383-2_1
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DOI: https://doi.org/10.1007/978-1-4613-9383-2_1
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