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非正则最大似然问题AI 解读

SUMMARY Four non-regular estimation problems are reviewed and discussed. One (the unbounded likelihood problem) involves distributions with infinite spikes, for which maximum likelihood can fail to give consistent estimators. A comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case. An application to the Box–Cox shifted power transform is given. The other three problems occur when the true parameter lies in some…

非线性回归中的嵌入模型AI 解读

SUMMARY A problem that is often encountered in non-linear regression is instability in the computation of parameter estimates. Such instability may arise from models with too many parameters, resulting in estimating equations that are ill conditioned and consequent problems of identification. This paper shows that in some cases these difficulties can be explained by the presence of an embedded model, a special case of the original model involving fewer parameters but one…

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参数经估计时使用 Moran 统计量的拟合优度检验AI 解读

Moran's log spacings statistic for testing goodness of fit is shown to have the same asymptotic distribution when parameters must be estimated from the sample as it does when parameters are known, provided the estimation is done efficiently. For small samples, a chi-squared approximation is given and shown to be accurate when estimation is carried out by minimizing Mdran's statistic itself regarded as a function of the unknown par ameters. A numerical example is given to…

非正则问题中的修正最大似然法AI 解读

SUMMARY Maximum likelihood (ML) estimation can break down for distributions like the three-parameter Weibull or gamma where one of the parameters is a limit of the range of the distribution. It is suggested that use of the product of densities for the likelihood function is a misapplication of the ML method in such non-regular cases, and that this is the reason for its failure. It is shown that ML works quite satisfactorily if the likelihood is corrected in an appropriate…

原点未知平移的连续单变量分布参数估计AI 解读

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…