Sensitivity of Selected Method of Estimation Based on the Lee-carter Model

Abstract

Efficiency and the unbiasedness structure of three method of estimation namely: the Weighted Least Square, Maximum Likelihood Estimation and the Method of Moment were examined in this study. Using three scenarios labelled as Case I, II & III; where Case I is model simulation based on the distributional properties of the Lee Carter model, Case II and III were majorly data contamination by self-inclusion of Outliers to the simulated dataset for High (Case II) and Low (Case III), respectively.  The behavioral patterns of the estimators were assessed at different sample sizes. Under Case I, it was noted that the larger the sample size n, the more the distribution tends to Normal but for Case II and III, the data gets inflated. The performance of each method of estimation was tested in accordance to the properties of estimators. MLE was best among the three estimators for the Lee Carter Model. The estimated parameters \(a_{x}\)  \(b_{x}\) and \(k_{t}\) were observed to approach the true parameter as the sample size increases.