ABSTRACT
We have limited our discussions mainly to the case of multivariate normal distributions. The cases of nonnormal and discrete distributions are equally important in practice and have been studied by various workers. For multinomial distributions the works of Matusita (1956), Chernoff (1956), Cochran and Hopkins (1961), Bunke (1966), and Glick (1969) are worth mentioning. For multivariate Bernouilli distributions we refer to Bahadur (1961), Solomon (1960, 1961), Hills (1966), Martin and Bradly (1972), Cooper (1963, 1965), Bhattacharya and Das Gupta (1964), and Anderson (1972). The works of Kendall (1966) and Marshall and Olkin (1968) are equally important for related results in connection with discrete distributions. The reader is also referred to the book edited by Cacoullos (1973) for an up-to-date account of research work in the area of discriminant analysis. Rukhin (1991) has shown that the natural estimator of the discriminant coefficient vector ? is admissible under quadratic loss function when S=s2I. Khatri and Bhavsar (1990) have treated the problem of the estimation of discriminant coefficients in the family of complex elliptically symmetric distributions. They have derived the asymptotic confidence bounds of the discriminatory values for the linear Fisher’s discrimination for the future complex observation from this family.
