Summary
The problem is to estimate the mean of the normal distribution under the situation where there is vague information that the mean might be equal to zero. A minimax property of the preliminary test estimator obtained by the use of AIC (Akaike information Criterion) procedure is proved under a loss function based on the Kullback-Leibler information measure.
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Nagata, Y., Inaba, T. Minimaxity of a preliminary test estimator for the mean of normal distribution. Ann Inst Stat Math 37, 437–442 (1985). https://doi.org/10.1007/BF02481111
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DOI: https://doi.org/10.1007/BF02481111