Studies on the optimality of methods of statistical sequential decisions

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Head investigator and each of the investigators obtained the research results concerning the title of this project directly or indirectly. The main results by head investigator are as follows :(1) We considered the problem of estimating a linear combination of unknown location and scale parameters of a negative exponential distribution. Given a class of estimators, we want to estimate the linear combination by using the sample of the smallest size such that the risk associated with them is not greater than a preassigned error bound. We proposed a sequential estimator and obtained the asymptotic expansion of the risk.(2) We considered the sequential point estimation problem of a linear combination of means of k populations. Our procedure was shown to have asymptotically less risk when compared with the existing procedure for some class of distributions.(3) We considered the sequential point estimation problem of a linear combination of unknown mean and standard deviation of a normal distribution under squared relative error plus linear cost as a loss function. We proposed a class of estimators and obtained second-order asymptotic expansions of the risk associated with the corresponding sequential estimators.