Sampling plans for middle or small sample size are often taken when the available data is not large enough. In this paper, a new quantile-based maximum likelihood estimation (QMLE) method for mean value estimation of a quasi-normal distribution is proposed. It takes the two endpoints of range as quasi-symmetric quantiles and fuses the concept of empirical and symmetric quantiles to define an objective function. It then follows the well-known "asymptotic minimax principle", which is a robust statistical method, to realize the optimization of the objective function. Simulation results confirmed that the proposed QMLE mean estimator outperforms the conventional sample mean estimator with about 40% uncertainty, or mean square error (MSE), reduction.
|Number of pages||6|
|Journal||IAENG International Journal of Applied Mathematics|
|State||Published - 1 Aug 2009|
- Asymptotic minimax principle
- Combined quantities
- Maximum likelihood estimation
- Sample mean