英文文献：Detecting Housing Submarkets using Unsupervised Learning of Finite Mixture Models-利用有限混合模型的无监督学习检测住房子市场
英文文献作者：Christos Ntantamis
英文文献摘要：
The problem of modeling housing prices has attracted considerable attention due to its importance in terms of households' wealth and in terms of public revenues through taxation. One of the main concerns raised in both the theoretical and the empirical literature is the existence of spatial association between prices that can be attributed, among others, to unobserved neighborhood effects. In this paper, a model of spatial association for housing markets is introduced. Spatial association is treated in the context of spatial heterogeneity, which is explicitly modeled in both a global and a local framework. The global form of heterogeneity is incorporated in a Hedonic Price Index model that encompasses a nonlinear function of the geographical coordinates of each dwelling. The local form of heterogeneity is subsequently modeled as a Finite Mixture Model for the residuals of the Hedonic Index. The identified mixtures are considered as the different spatial housing submarkets. The main advantage of the approach is that submarkets are recovered by the housing prices data compared to submarkets imposed by administrative or geographical criteria. The Finite Mixture Model is estimated using the Figueiredo and Jain (2002) approach due to its ability in endogenously identifying the number of the submarkets and its efficiency in computational terms that permits the consideration of large datasets. The different submarkets are subsequently identified using the Maximum Posterior Mode algorithm. The overall ability of the model to identify spatial heterogeneity is validated through a set of simulations. The model was applied to Los Angeles county housing prices data for the year 2002. The results suggests that the statistically identified number of submarkets, after taking into account the dwellings' structural characteristics, are considerably fewer that the ones imposed either by geographical or administrative boundaries.

由于对家庭财富和通过税收获得的公共收入的重要性，建立住房价格模型的问题引起了相当多的关注。在理论和经验文献中提出的主要关注之一是价格之间的空间关联的存在，可以归因于未观察到的邻里效应。本文介绍了一个住宅市场空间关联模型。空间关联是在空间异质性的背景下处理的，而空间异质性是在全局和局部框架中明确建模的。全球形式的异质性包含在一个享乐价格指数模型中，该模型包含每个住宅地理坐标的非线性函数。局部形式的异质性随后被建模为一个有限混合模型的残差的特征指数。所识别的混合物被认为是不同的空间住房子市场。这种方法的主要优点是，次级市场与行政或地理标准所规定的次级市场相比，可以通过住房价格数据恢复。有限混合模型的估计使用Figueiredo和Jain(2002)方法，因为它能够内生地识别子市场的数量，并且它的计算效率允许考虑大数据集。然后利用最大后验模算法对不同的子市场进行识别。通过一系列的模拟验证了该模型识别空间异质性的整体能力。该模型应用于洛杉矶县2002年的房价数据。结果表明，在考虑了住宅的结构特征后，统计上确定的次级市场数量要比由地理或行政边界设置的次级市场数量少得多。