Studies on efficiency of statistical methods of sequential estimation

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Head investigator and each of investigators obtained the results which are concerned with the title of this project directly or indirectly. The main results given by head investigator are as follows.(1) We considered the minimum risk sequential point estimation problem for a function of the scale parameter of an exponential distribution subject to the loss function given as a sum of the squared error and a linear cost. We want to estimate the function by using the sample size which minimizes the risk of the expectation of the loss. Then the smallest sample size contains the unknown parameter. Therefore, we proposed a fully sequential procedure and gave the second-order expansion of the expected sample size and risk when the cost per unit observation tended to zero.(2) We considered the problem of estimating a function of two scale parameters from two exponential populations. We want to construct a confidence interval of the function with given length and confidence coefficient. The asy … More mptotic smallest sample size contains the unknown parameters, so we proposed a fully sequential sampling procedure and sequential confidence intervals. We showed that these sequential confidence intervals have asymptotic consistency and gave the second-order asymptotic expansion of the expected sample size.(3) We considered sequential bounded risk point estimation of the ratio of scale parameters of two exponential distributions subject to the loss function given as the squared error. We wish to estimate the ratio under the condition that the risk of the expected loss is bounded by a preassigned positive constant. The smallest sample size which satisfies the condition includes the unknown parameters. Therefore, we proposed a fully sequential sampling scheme and provided second order approximation of the expected sample size and the risk of the sequential procedure. We also proposed a bias corrected sequential procedure to reduce the risk and obtained a second order approximation of its risk. Less