ESTIMATING FUNCTION WITH ASYMPTOTIC BIAS AND ITS ESTIMATOR

YOSHIJI TAKAGI^{1} AND NOBUO INAGAKI^{2}

1College of Integrated Arts and Science, University of Osaka Prefecture, Sakai, Osaka 593, Japan 2Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan

(Received September 9, 1991; revised September 11, 1992)

Abstract. We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics.

Key words and phrases: Estimating function, asymptotic bias, asymptotic normality, order statistics, ridge estimator function, maximum posterior likelihood estimator.