Frontiers of Mathematics in China >
Probability density estimation with surrogate data and validation sample
Received date: 21 Aug 2012
Accepted date: 19 Nov 2012
Published date: 01 Jun 2013
Copyright
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.
Key words： Measurement error; asymptotic normality; convergent rate
Qihua WANG , Wenquan CUI . Probability density estimation with surrogate data and validation sample[J]. Frontiers of Mathematics in China, 2013 , 8(3) : 665 -694 . DOI: 10.1007/s11464-013-0267-0
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