Robust diagnostic and robust estimation methods for fixed effect panel data model in presence of high leverage points and multicollinearity

The Diagnostic Robust Generalized Potential based on Minimum Volume Ellipsoid (MVE) is proposed in linear regression to detect high leverage points (HLPs). However, it takes a very long computational running time and also has small rate of swamping and masking effects. Hence the Improvised Diagnostic Robust Generalized Potential based on Index Set Equality (IDRGP (ISE)) is proposed to linear and fixed effect panel data model. The results indicate that IDRGP(ISE) successfully identify high leverage points with the reduction in the rate of swamping and masking effects and has less computational running time. To date no research has been done to identify HLPs for panel data. Hence, to close the gap in the literature we propose Within Group Improvised Diagnostic Robust Generalized Potential (WIDRGP). It is very successful in detecting HLPs and relatively fast to compute. The Generalized M-estimator (GM6) is the widely used method to overcome the problem of HLPs for multiple linear regression model. However, this method is less efficient since it is based on Robust Mahalanobis Distance RMD- MVE as an initial π–weight function. Its efficiency decreases as the number of good leverage points increases. Hence, the Generalized M-estimator (GM) based on Fast Improvised Generalized Studentized Residuals (FIMGT), denoted as (GM-FIMGT) is developed. The results show that the GM-FIMGT is highly efficient and relatively fast. A robust Within Group GM estimator based on FIMGT estimator (WGM-FIMGT) for fixed effect panel data model is proposed. The findings indicate that the WGM-FIMGT is very efficient compared to the existing estimators. Thus far, no research has been done on the detection of multicollinearity for fixed effect panel data models in the presence of HLPs. Hence, Robust Variance Inflation Factor based on GM-FIMGT (RVIF(GM-FIMGT)) is formulated. The results of the study show that it is very effective in detecting multicollinearity in the presence of HLPs. The Jackknife ridge regression is one of the commonly used method to remedy the problem of multicollinearity. Nonetheless, it is very sensitive to outliers and HLPs. Hence Robust Jackknife ridge regression based on FIMGT (RJFIMGT) is developed to rectify the combined problem of multicollinearity and high leverage points. The results of the study indicate that the RJFIMGT is the most efficient method when multicollinearity problem come together with the presence of HLPs. Still no research has been done on the parameter estimation of fixed effect panel data model in the presence of multicollinearity and HLPs. Thus the within Group Robust Jackknife ridge regression based on FIMGT (WRJFIMGT) is developed to close the gap in the literature. The findings signify that WRJFIMGT provides the best estimates when multicollinearity and HLPs are present in a data set

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