Maximum L_q-Likelihood Estimation of Reproductive Dispersion Linear Models

Reproductive dispersion linear models (RDLMS) are the natural generalization of statistical models such as linear regression models, generalized linear models and exponential linear models. Maximum L_q-likelihood estimation (ML_qE) is a generalization of maximum likelihood estimation. Building on Fahrmeir et al., we establish weak and strong consistency as well as asymptotic normality of the ML_qE of RDLMS, thereby extending the existing results. A simulation example shows that our estimation method is effective is effective the maximum Lq-likelihood estimation is robust.