Abstract
In this article, we consider a class of kernel quantile estimators which is the linear combination of order statistics. This class of kernel quantile estimators can be regarded as an extension of some existing estimators. The exact mean square error expression for this class of estimators will be provided when data are uniformly distributed. The implementation of these estimators depends mostly on the bandwidth selection. We then develop an adaptive method for bandwidth selection based on the intersection confidence intervals (ICI) principle. Monte Carlo studies demonstrate that our proposed approach is comparatively remarkable. We illustrate our method with a real data set.
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Supported by Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant Nos. 10XNL018, 10XNK025), National Natural Science Foundation of China (Grant No. 11271368), Beijing Planning Office of Philosophy and Social Science (Grant No. 12JGB051), China Statistical Research Project (Grant No. 2011LZ031), and Project of Ministry of Education supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130004110007), the Key Program of National Philosophy and Social Science Foundation Grant (No. 13AZD064)
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Fan, J.Y., Tang, M.L. & Tian, M.Z. Kernel quantile estimator with ICI adaptive bandwidth selection technique. Acta. Math. Sin.-English Ser. 30, 710–722 (2014). https://doi.org/10.1007/s10114-014-1233-9
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DOI: https://doi.org/10.1007/s10114-014-1233-9