In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based correntropy estimators as special cases. An analysis of the robustness properties is then provided. The analysis includes a quantitative characterization of the informativity degree of the regression which is appropriate for studying the stability of the estimator. Using this tool, a sufficient condition is expressed under which the parametric estimation error is shown to be bounded. Explicit expression of the bound is given and discussion on its numerical computation is supplied. For illustration purpose, two special cases are numerically studied.