MLEce: Statistical inference for asymptotically efficient closed-form estimators in R

Abstract

Maximum likelihood estimation is a classical method with useful properties like efficiency, consistency, and asymptotic normality. However, the maximum likelihood estimator (MLE) cannot be in closed form in many distributions. Therefore, it is obtained by iterative methods, such as the Newton–Raphson algorithm, which is time consuming and unrobust. For three multivariate distributions (bivariate Weibull, bivariate gamma and multivariate Dirichlet distributions) where the corresponding MLEs are not in closed forms, the R package MLEce is developed to provide new efficient estimators with asymptotic normality and efficiency like the MLE. Along with MLE and method of moment estimator (MME), MLEce package conducts point estimation (closed-form efficient estimator), random sample generation, goodness-of-fit test, and confidence interval estimation. Simulations and real data examples are provided to help us understand how to use MLEce.

Keywords

• Closed-form estimator
• Asymptotically efficient estimator
• Statistical inference
• MLE
• MME