THE NONEXISTENCE OF PROCEDURES WITH BOUNDED PERFORMANCE CHARACTERISTICS IN CERTAIN PARAMETRIC INFERENCE PROBLEMS

YOSHIKAZU TAKADA

Department of Mathematics, Faculty of Science, Kumamoto University, Kumamoto 860-0862, Japan

(Received November 21, 1996; revised May 29, 1997)

Abstract. This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.

Key words and phrases: Fixed-width confidence interval, location-scale family, scale family, inverse Gaussian distribution, errors-in-variables regression model, calibration problem.