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Probability density estimation with surrogate data and validation sample |
Qihua WANG1, Wenquan CUI2( ) |
| 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2. Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China |
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Abstract The probability density estimation problem with surrogate data and validation sample is considered. A regression calibration kernel density estimator is defined to incorporate the information contained in both surrogate variates and validation sample. Also, we define two weighted estimators which have less asymptotic variances but have bigger biases than the regression calibration kernel density estimator. All the proposed estimators are proved to be asymptotically normal. And the asymptotic representations for the mean squared error and mean integrated square error of the proposed estimators are established, respectively. A simulation study is conducted to compare the finite sample behaviors of the proposed estimators.
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| Keywords
Measurement error
asymptotic normality
convergent rate
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Corresponding Author(s):
CUI Wenquan,Email:qhwang@amss.ac.cn
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Issue Date: 01 June 2013
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