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This book deals with Introduction, Basic Concepts of Least Absolute Deviation (LAD), Brief Review of Regression Theory. It presents the work related to Estimation of LAD versus Linear and Nonlinear Regression Models, LAD Estimation versus Nonlinear Regression Model with Heteroscedasticity Errors and with Robust Regression Models are also discussed. Further, it contains Estimation of the general Linear and Nonlinear Regression Models with Auto-Correlated Errors.