LINEX UNBIASEDNESS IN A PREDICTION PROBLEM

YUSHAN XIAO

Graduate School of Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan

(Received November 12, 1998; revised July 16, 1999)

Abstract. A statistical prediction problem under LINEX loss function is considered. Some results about LINEX-unbiased predictor are derived and the best LINEXunbiased predictor is given. We also show that the best risk-unbiased predictor is equal to the best equivariant predictor in the location family.

Key words and phrases: Prediction problem, risk unbiasedness, LINEX loss function, adequate statistic, Rao-Blackwell theorem, location family, equivariant predictor.