Bayesian model averaging of possibly similar nonparametric densities

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• 作者：Alan P. Ker ; Yong Liu
• 关键词：Small sample estimator ; Nonparametric density estimation ; Borrowing information
• 刊名：Computational Statistics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：32
• 期：1
• 页码：349-365
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods;
• 出版者：Springer Berlin Heidelberg
• ISSN：1613-9658
• 卷排序：32

文摘

We consider an alternative or expanded data environment where we have sample data from a set of densities that are thought to be similar (as measured by Kullback–Leibler divergence). While estimation methods could easily be applied to each individual sample separately, the purpose of this manuscript is to develop an estimator that: (1) offers greater efficiency if in fact the set of densities are similar while seemingly not losing any if the set of densities are dissimilar; (2) does not require knowledge about the form or extent of similarities between the densities; (3) can be used with parametric or nonparametric methods; (4) allows for correlated data; and (5) is relatively easy to implement. Simulations indicate finite sample performance—in particular small sample performance—is quite promising. Interestingly, in the case where both similar and dissimilar densities are in the set of possible densities, the proposed estimator appropriately puts weight on the similar and not on the dissimilar densities. We apply the proposed estimator to recover a set of county crop yield densities and their corresponding crop insurance premium rates.