GMM Estimation of Mixtures from Grouped Data
GMM Estimation of Mixtures from Grouped Data
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根据分组数据对混合物进行 GMM 估计
DOI：
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发表时间：
2012
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通讯作者：
William E. Griffiths and Gholamreza Hajargasht
中科院分区：
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作者：
William E. Griffiths and Gholamreza Hajargasht
我们展示了Hajargasht等人（2012）为估计分组数据的收入分布而开发的广义矩量法（GMM）框架如何适用于估计混合数据。这种方法可以用来估计任何混合分布，其中混合分量的矩和矩分布函数可以用这些分量的参数来表示。给出了对数正态密度和伽马密度混合所需的表达式；在我们的实证工作中，我们着重于对数正态分布的混合估计。对中国农村、中国城市、印度农村、印度城市、巴基斯坦、俄罗斯、南非、巴西和印度尼西亚的收入分布估计了两分量和三分量对数正态混合。在矩条件的拟合优度和有效性方面，它们的性能与广义beta （GB2）分布的性能进行了比较。我们发现三组分对数正态混合总是优于GB2分布，而两组分混合则不是。对于巴西和印度尼西亚，我们有单一的观测值，这使得有可能将一组完整的单一观测值的混合物的最大似然估计与分组数据后获得的GMM估计进行比较。两种方法的估计结果具有可比性，从而支持了GMM方法的有效性。
We show how the generalized method of moments (GMM) framework developed in Hajargasht et al. (2012) for estimating income distributions from grouped data can be adapted for estimating mixtures. This approach can be used to estimate a mixture of any distributions where the moments and moment distribution functions of the mixture components can be expressed in terms of the parameters of those components. The required expressions for mixtures of lognormal and gamma densities are provided; in our empirical work we focus on estimation of mixtures of lognormal distributions. Two- and three-component lognormal mixtures are estimated for the income distributions of China rural, China urban, India rural, India urban, Pakistan, Russia, South Africa, Brazil and Indonesia. Their performance, in terms of goodness-of-fit and validity of moment conditions, is compared with that of a generalized beta (GB2) distribution. We find that the three-component lognormal mixture always outperforms the GB2 distribution, but the two-component mixture does not. For Brazil and Indonesia we have single observations, making it possible to compare maximum likelihood estimation of the mixtures from a complete set of single observations with GMM estimates obtained after grouping the data. Estimates from both procedures are found to be comparable, lending support to the usefulness of the GMM approach.