AUTHORS: Jun Hu, Nitis Mukhopadhyay
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Under the squared error loss plus linear cost of sampling, we revisit the minimum risk point estimation (MRPE) problem for an unknown normal mean µ when the variance σ 2 also remains unknown. We begin by defining a new class of purely sequential MRPE methodologies based on a general estimator Wn for σ satisfying a set of conditions in proposing the requisite stopping boundary. A number of desirable asymptotic first-order and second-order properties associated with this new class of estimation methodologies have been investigated. After such general considerations, we include a number of substantial illustrations where we respectively substitute appropriate multiples of Gini’s mean difference and the mean absolute deviation in the place of the general estimator Wn.
KEYWORDS: Minimum Risk Point Estimation, Regret Expansion, Risk Efficiency, Sequential Sampling, Simulations
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