Influence diagnostics in the linear model with Kibria–Lukman estimator

Le résumé fourni par la source

Influential observation detection is an important aspect of regression analysis. When influential points and multicollinearity were present, then certain diagnostic methods could detect significant points; however, in certain instances, these methods were unable to find influential points when the multicollinearity among the explanatory variables was moderate. This means that when the problem is curtailed, they become less susceptible to multicollinearity. Therefore, the effective methods that performed better than the rest show that they remain strong even after the abnormality is managed. The goal of this study is to develop some influential observation detection methods in the new one-parameter ridge estimator known as the Kibria–Lukman (K-L) estimator. The K-L influential methods and the hat matrix for the K-L estimator were used in the following conventional diagnostic tools; Cook’s Distance (CKD), DFFITs (DFT), COVRATIO (CVR), and Hadi’s measure (HAD). Also, approximate case deletion formulas for both CKD and DFT were derived. The performance of these diagnostics is evaluated with the support of a simulation study and a real application. Results suggested that the influential observation detections are very sensitive to the multicollinearity. The findings showed that the CVR under the K-L estimator gives better performance for smaller sample size. While for larger sample size, dispersion, and high multicollinearity, the HAD with K-L estimator gives a better performance as compared to other methods.

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