Debiasing UTO Estimator: Methods and Application to Climate Change Data Sets

Estimators with two biasing parameters are very popular because they incorporate the benefits of both biasing parameters in dealing with the problem of multicollinearity. Due to the rising number of two‐parameter estimators, the issue of increasing bias becomes more visible. Hence, the usage of techniques that reduce the bias of the biased estimators is inevitable. From this perspective, in this article, we handle the bias reduction of the UTO estimator, a two‐parameter estimator that is recently defined and yields remarkable results. Within this respect, first, we apply the jackknife technique to reduce the bias of the UTO estimator. Secondly, we define the debiased UTO (D‐UTO) estimator with adjustment for the bias of the UTO estimator. Then, we perform some theoretical comparisons according to bias and mean square error criterion for the new D‐UTO estimator. To derive optimal estimators of biasing parameters of the D‐UTO estimator, we offer two methods, one of which is a classical method and the other one is a mathematical programming method. In the classical method, mean square error is minimized, and the method is summarized in two paths. While defining the mathematical programming approach, mean square error and squared bias are taken into consideration in two different scenarios. In the application part, two data sets about climate change, which is a popular topic, and a Monte Carlo simulation experiment are examined. According to the outcomes, the D‐UTO estimator outperforms its competitors regarding both the squared bias and mean square error.