Sequential estimation of a linear function of mean vectors

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Abstract
Let π1,...,πk be k independent populations where we assume that the ith population distribution is The parameters and σi ε (0,∞) for i = l,...,k are all assumed unknown, but H1einf:,...,Hk are known positive definite p&z.Times;p matrices. We estimate parameters of the form where ci's are known nonzero constants for i = 1,...,k, by means of ellipsoidal confidence regions. Various two-stage and sequential procedures are proposed and some of their exact and asymptotic properties are studied. Statistical methods and some of their characteristics are discussed both when H1,...,Hk are simultaneously diagonalizable as well as when they are not.