Point and Interval Estimation for Gaussian Distribution, Based on Progressively Type-II Censored Samples

The likelihood equations based on a progressively Type-II censored sample from a Gaussian distribution do not provide explicit solutions in any situation except the complete sample case. This paper examines numerically the bias and mean square error of the MLE, and demonstrates that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic $s$-normality are unsatisfactory, and particularly so when the effective sample size is small. Therefore, this paper suggests using unconditional simulated percentage points of these pivotal quantities for constructing $s$-confidence intervals. An approximation of the Gaussian hazard function is used to develop approximate estimators which are explicit and are almost as efficient as the MLE in terms of bias and mean square error; however, the probability coverages of the corresponding pivotal quantities based on asymptotic $s$-normality are also unsatisfactory. A wide range of sample sizes and progressive censoring schemes are used in this study.