On the estimation of population mode in time-scaled surveys using ranked auxiliary information

The existing mode estimators are traditionally based on one-time sample surveys, which may adversely affect the estimates due to measurement errors arising during the interviewing process. In contrast, time-scaled surveys yield more efficient and reliable estimates for the population mode compared to traditional one-time surveys. This study proposes a novel unbiased difference-type estimator for population mode in the context of time-scaled surveys. The performance is evaluated using two real datasets supplemented by an extensive simulation study. The results indicate that the proposed estimator consistently outperforms commonly used existing mode estimators. Among all estimators, the ratio estimator is biased when a first-order approximation is used. Overall, the proposed estimator provides reliable and efficient alternatives for mode estimation in time-scaled survey settings where ranked auxiliary information is available. The simulation study and graphical presentations further confirm the superiority of the proposed estimator under time-scaled surveys.