Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin
提出一种估计连续单变量分布参数的方法，特别适用于原点未知平移的情况（如三参数对数正态、伽马和威布尔模型），在极大似然估计失效时仍能给出一致且渐近有效的估计。
Summary A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed method are described. In particular it is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist. Moreover it gives consistent, asymptotically efficient estimators in situations where ML fails. Examples are given including numerical ones showing the advantages of the method.