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Bayesian model averaging of possibly similar nonparametric densities

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  • Alan P. Ker

    (University of Guelph)

  • Yong Liu

    (University of Guelph)

Abstract

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.

Suggested Citation

  • Alan P. Ker & Yong Liu, 2017. "Bayesian model averaging of possibly similar nonparametric densities," Computational Statistics, Springer, vol. 32(1), pages 349-365, March.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0700-4
    DOI: 10.1007/s00180-016-0700-4
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    References listed on IDEAS

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    1. Ardian Harri & Keith H. Coble & Alan P. Ker & Barry J. Goodwin, 2011. "Relaxing Heteroscedasticity Assumptions in Area-Yield Crop Insurance Rating," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(3), pages 703-713.
    2. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    3. Peter J. Green & Sylvia Richardson, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 355-375, June.
    4. Ker, Alan P., 2016. "Nonparametric estimation of possibly similar densities," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 23-30.
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    Cited by:

    1. Zongyuan Shang & Alan Ker, 2021. "Two generalized nonparametric methods for estimating like densities," Computational Statistics, Springer, vol. 36(1), pages 113-126, March.
    2. Yong Liu & Alan P. Ker, 2021. "Simultaneous borrowing of information across space and time for pricing insurance contracts: An application to rating crop insurance policies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 231-257, March.
    3. A. Ford Ramsey & Yong Liu, 2023. "Linear pooling of potentially related density forecasts in crop insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(3), pages 769-788, September.

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