The semi-parametric MLE in linear regression with right-censored data

Consider the linear regression model, Y_i = β′X _i + ε_i, i = 1, . . . , n, where Y_i maybe right censored and ε_i has an unknown cdf F_o. The semi-parametric MLE (SMLE) of β, denoted by β̃_n, has not been studied, and there is no known method in the literature for finding β̃_n. β̃_n cannot be obtained by standard numerical methods, including the Newton-Raphson method and the Monte Carlo method. We propose a feasible non-iterative algorithm for β̃_n. Simulation results suggest that β̃ _n is consistent if F_o is continuous and β̃ _n is efficient if F_o has discontinuity points. A consistency and efficiency result is established under certain regularity conditions. We apply the SMLE to three data sets of sizes 10, 69 and 374, respectively. The results indicate that the SMLE may have advantages over the Buckley-James estimator in applications.