In this paper, the maximum Lq-likelihood estimator (MLqE), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30-35] is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLqE can successfully trade bias for precision, resulting in a substantial reduction of the mean squared error. When the sample size is large and q tends to 1, a necessary and sufficient condition to ensure a proper asymptotic normality and efficiency of MLqE is established.
- Asymptotic efficiency
- Exponential family
- Maximum Lq-likelihood estimation
- Nonextensive entropy
- Tail probability estimation