Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors

The ordinary Nonlinear Least Squares (NLLS) and the Maximum Likelihood Estimator (MLE) techniques are often used to estimate the parameters of nonlinear models. Unfortunately, many researchers are not aware of the consequences of using such estimators when outliers are present in the data. The problems get more complex when the assumption of constant error variances or homoscedasticity is violated. To remedy these two problems simultaneously, we proposed a Robust Multistage Estimator (RME). The heterogeneouity of error variances is considered when the variances of residuals follows a parametric functional form of the predictors. Both Nonlinear model function parameters and variance model parameters must be robustified. We have incorporated the MM, the generalized MM and the robustified Chi-Squares Pseudo Likelihood function in the formulation of the RME. The results of the study reveal that the RME is more efficient than the existing methods. The thesis also addresses the problems when the assumptions of the independent error terms are not met. We proposed a new Robust Two Stage (RTS) estimator in this regard. The proposed method is developed by incorporating the generalized MM estimator in the classical two stage estimator. The performance of the RTS is more efficient than other existing methods revealed by having the highest robustness measures. We also proposed two outlier identification measures in nonlinear regression. The Tangent leverage, the NLLS, the M and the MM estimators are incorporated in the formulation of the first outlier identification measures. The formulation of the second measure is based on the differences between the derived robust Jacobian Leverage and Tangent leverage. Both proposed measures are very successful to identify the correct outliers. Finally, we proposed statistics practitioners to use the formal modeling algorithms to get better inferences. We also suggest them to employ appropriate robust methods for further analysis once a correct model has been chosen. The results of the study based on real data signify that the robust estimator is more efficient indicated by lower values of standard errors when compared to the classical estimator

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