SOME PROBLEMS IN THE CHARACTERIZATION OF THE WISHART DISTRIBUTION
DOI:
https://doi.org/10.31642/JoKMC/2018/010112Keywords:
WISHART DISTRIBUTION, characterizationAbstract
Under the multivariate linear model{Y , Xb ,åÄV }, A number of characterization of the distribution of
i X have been made based on the properties of the statistics 1 Y and 2 Y when 1 Y and 2 Y be two linear functions defined on R1 as follows n n Y = a X + ....+ a X 1 1 1 and n n Y = b X + .....+ b X 2 1 1 . Generalizations of these problems to the multivariate case have been made by several authors by extending the techniques used in the univariate case. In my paper I shall consider some other generalization, which possibly require development of new techniques ,if 1 2 X , X be independent and identically distributed p-vector r.v.,s such that ( \ ) 0 1 2 1 2 E X - AX X + B¢X = ,where A and B are nonsingular matrices. In special case when A = B-1 , A is symmetric and the egen values do not take values ±1. Under these conditions that 1 X has an m.n.d. in the present paper we shall consider a few other cases.
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Eaton Morris, L.and Pathak, P.K.(1969). A characterization of the normal law in Hilbert space. Sannkya 31,259-268.
Dan Geiger, David Heckerman(1980). A characterization of the bivariate Wishart distribution probality and Mathematical Statistics Vol. 18, Fasc. 1 (1980), pp. 119–131
Hede, C. C. (1970). Characterization of normal law by the symmetry of a certain conditional distribution. Sankyha 32,115-118.
Kagan, A .M., Linnik, Yu.V. and Rao , C.R.(1972,1973).Characterization problems of Mathematical Statistics. Russian edition , 1972, Academy Nauk, Mosscow ; English edition , 1973, John Wiley , New York.
Kharri , C.G.and Rao , C.R.(1972). Functional equations and characterization of probability laws through linear functions of random variables . J. Multivariate Analysis 2,162- 173.
Kharri , C.G.and Rao , C.R. (1974).Characterization of multivariate normal distribution by constancy of regression of one linear function on another (under preparation).
Klebanov, L.B.(1970).on a functional equation . Sankhya 32,387-392.
Linnik, Yu,V. .(1953). Linear forms ans statistical criteria. I and II (in Russian). Ukrain .Mat .Zhurnal 5,207-243 and 247-290.
Ramachandran , B. and Rao,C.R.(1968). Some results on characterizations of the normal and generalized stable laws.Sankyha A 30, 125-140.
Ramachandran , B. and Rao,C.R. (1970).Solutions of a functional equation arising in some regression problems and a characterization of the Cauchy law, Sankhya A 32,1-30.
Rao ,C.R.(1969).Some characterizations of the multivariate normal distribution. Multivariate Analysis-II.P321-328 Ed .P.R.Krishnaih , Academic Press ,New York.
Rao ,C.R.( (1973). Linear Statistical Inference and its Applications. Jhon Wiley , New York.
Rao ,C.R.(1974c) .Functional equations and characterization of probability distributions.(Invited address,world Congress of Mathematics, 1974, Vancouver).
Robbins ,J.W.(1971).A structural stability theorem.T.A.M.S.,447-493.
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