Robust diagnostic and parameter estimation for multiple linear and panel data regression models

The Influential Distance (ID) is proposed to identify multiple influential observations (IOs) in linear regression. However, the method not only considered good leverage observations (GLOs) as IOs, but also takes long computational running time with high rate of swamping and masking effects. Fast Improvised Influential Distance (FIID) is proposed to overcome these shortcomings. The results indicate that FIID successfully identified and classified GLOs and IOs with less computational running time, no masking effect and smaller rate of swamping. The presence of high leverage points (HLPs) and violation of the assumption of homoscedasticity are very common in analyzing data in linear and panel data regression models. To remedy this problems weighted least squares (WLS) based on FIID weighting method for Heteroscedasticity Consistent Covariance Matrix (HCCM) estimator is developed. The results obtained from simulation study and real data sets indicate that the proposed method is superior compared to the existing methods. The presence of outlying observations in a data set causes heteroscedasticity in a homoscedastic data set and vice versa. To know the type of outliers that are responsible for these irregularities is very important so that appropriate measure will be taken. To bridge the gap in the literature, we have successfully proposed robust White test to detect heteroscedasticity and identifies the types of outliers that causes and hide heteroscedasticity termed heteroscedasticity-enhancing and heteroscedasticityreducing observations (HEO and HRO), respectively. Furthermore, we proposed appropriate remedial measures for both HEO and HRO denoted by GM-FIID and ITSRWLS, respectively. The results of the simulation study show that the proposed methods are efficient and consistent than the existing methods. The panel data estimators for both fixed and random effect models becomes bias and causes inconsistency in variance-covariance matrix when there exist heteroscedasticity of unknown form and high leverage points in a data set. To date no research has been done to address this problem. To fill-in the gap in the literature we proposed a WLS estimation technique for both fixed and random effect model based on RHCCM estimator with FIID weighting method. The MM-Centering technique is employed instead of mean centering to reduce the effect of HLPs. The results of simulation study and real data sets indicate that weighted least squares based on FIID (WLSFIID) was found to be the best method. The classical Hausman pretest is used to choose between random and fixed effect panel data models. In the presence of heteroscedastic error variances and high leverage points (HLPs) or IOs in a data set, the right model may not be correctly identified. To the best of our knowledge no research has been done to address this issue. We proposed a robust Hausman pretest denoted as RHTFIID based on FIID and Robust Heteroscedasticity Consistent Covariance Matrix (RHCCM) estimator to remedy the problem. The results of simulation and real data set indicate that the proposed method was found to perform better than the conventional Hausman pretest.

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