Optimisation of the Maximum Likelihood Method Using Bias Minimisation

Maximum likelihood (ML) is a popular and widely used statistical method, and while it is effective, its major short-comings are that it is a biased and non robust estimator. This paper proposes a formal establishment of an optimisation of ML (OML) by approximating the true distribution minimising the bias, and exploiting the underlying relationship between ML and the maximum entropy method. OML exposes the inefficiency of the classical ML in the orthogonal least square error minimisation sense, for a number of finite sample datasets. The robustness of the proposed OML method in finding an estimate within the boundaries of the parameter space is also proven. Under the same conditions, OML consistently provides a more global and efficient estimation, so both theoretically and empirically establishing its superiority over ML in terms of efficiency and robustness