Semiparametric maximum likelihood estimation with estimating equations
(SMLE) is more flexible than the traditional methods such as the parametric maximum likelihood estimation, Cox's proportional hazards model, accelerated failure time model, quasi-likelihood, and generalized estimating equations with much less restrictions on distributions and regression-models. The needed information about distribution and regression structures is incorporated in estimating equations of the SMLE to improve the estimation quality of nonparametric methods. The likelihood of the SMLE in censored data cases involve several complicated implicit functions without closed-form expressions, and the first derivatives of the log-profile-likelihood cannot be expressed as summations of independent and identically distributed random variables.

For group-censored data and continuos data, it is verified that all the implicit functions are well defined, and the asymptotic distributions of the SMLE for model parameters and lifetime distributions are obtained.

A real life example with HIV data is presented to illustrate the application of SMLE method.