Robust weighted likelihood estimation of exponential parameters

The problem of estimating the parameter of an exponential distribution when a proportion of the observations are outliers is quite important to reliability applications. The method of weighted likelihood is applied to this problem, and a robust estimator of the exponential parameter is proposed. Interestingly, the proposed estimator is an α-trimmed mean type estimator. The large-sample robustness properties of the new estimator are examined. Further, a Monte Carlo simulation study is conducted showing that the proposed estimator is, under a wide range of contaminated exponential models, more efficient than the usual maximum likelihood estimator in the sense of having a smaller risk, a measure combining bias & variability. An application of the method to a data set on the failure times of throttles is presented.