WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 18, 2019
A Class of Purely Sequential Minimum Risk Point Estimation Methodologies with Second-Order Properties
Authors: ,
Abstract: 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 $$W_{n}$$ 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 $$W_{n}$$.
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Keywords: Minimum Risk Point Estimation, Regret Expansion, Risk Efficiency, Sequential Sampling, Simulations
Pages: 407-414
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #49