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Moderate deviations for deconvolution kernel density estimators with ordinary smooth measurement errors

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  • Song, Weixing

Abstract

In this paper, we establish the pointwise and uniform moderate deviations limit results for the deconvolution kernel density estimator in the errors-in-variables model, when the measurement error possesses an ordinary smooth distribution. The results are similar to the moderate deviations theorems for the classical kernel density estimators, but a factor related to the ordinary smooth order is needed to account for the measurement errors.

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  • Song, Weixing, 2010. "Moderate deviations for deconvolution kernel density estimators with ordinary smooth measurement errors," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 169-176, February.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:3-4:p:169-176
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    References listed on IDEAS

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    1. Djamal Louani, 1998. "Large Deviations Limit Theorems for the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 243-253, March.
    2. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2009. "Nonparametric Prediction in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 993-1003.
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    Cited by:

    1. Zhao, Shoujiang & Liu, Qiaojing, 2012. "Moderate deviations for some nonparametric estimators with errors in variables," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1175-1184.

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