RESEARCH ARTICLE

Probability density estimation with surrogate data and validation sample

  • Qihua WANG 1 ,
  • Wenquan CUI , 2
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  • 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

Received date: 21 Aug 2012

Accepted date: 19 Nov 2012

Published date: 01 Jun 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

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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