A Monte Carlo Investigation of Confidence Intervals for a Nondecreasing Series

We consider the problem of estimating a time series of population means from a series of sample surveys when the means are known to be nondecreasing. We introduce the standard survey estimators of the series of means, which are not guaranteed to be nondecreasing. We employ the Pool Adjacent Violators Algorithm (PAVA) to turn the series of standard survey estimates into a nondecreasing series. We introduce five methods of constructing confidence intervals for the series of non-decreasing means: normal-theory intervals based on the standard survey point estimator of the mean and the Taylor series estimator of its variance; normal-theory intervals based on the nondecreasing PAVA estimator of the mean and a unique jackknife estimator of its variance developed here (jackknife-[Formula: see text]); intervals similar to the aforementioned method but based on Student’s-[Formula: see text] distribution (jackknife-[Formula: see text]); analytical intervals due to Morris; and simultaneous confidence limits due to Korn. We report the results of a Monte Carlo simulation and assess the methods’ performance under various scenarios. Jackknife-[Formula: see text] intervals exhibited coverage probabilities that are near the nominal value. Taylor, jackknife-[Formula: see text], and Korn intervals found coverage below the nominal value while Morris intervals were excessively conservative. Jackknife intervals were much narrower than Taylor intervals.