Sequential Minimum Risk Point Estimation of the Parameters of an Inverse Gaussian Distribution

SYNOPTIC ABSTRACT In the first part of this article, a minimum risk estimation procedure is developed for estimating the mean μ of an inverse Gaussian distribution having an unknown scale parameter λ. A weighted squared-error loss function is assumed, and we aim at controlling the associated risk function. First and second-order asymptotic properties are also established for our stopping rule. The second part deals with developing a minimum risk estimation procedure for estimating the scale parameter λ of an inverse Gaussian distribution. We make use of a squared-error loss function here. The failure of a fixed sample size procedure is established and, hence, some sequential procedures are proposed to deal with this situation. For this estimation problem, we make use of the uniformly minimum variance unbiased estimator (UMVUE) and the minimum mean square estimator (MMSE) of the associated parameters. Second-order approximations are derived for the sequential procedures and improved estimators are proposed.