Distribution estimation with smoothed auxiliary information |
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Authors: | Xu Liu Ahmad Ishfaq |
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Institution: | Xu Liu 1,2,Ahmad Ishfaq 2 1 Department of Statistics,Yunnan University,Kunming 650091,China 2 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China |
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Abstract: | Distribution estimation is very important in order to make statistical inference for parameters or its functions based on
this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,
for example, a symmetric distribution of this variable. A smoothing technique is employed to handle the non-differentiable
function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution
estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient
than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate
the finite sample performance of the proposed estimators. |
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Keywords: | Auxiliary information Empirical likelihood Estimating equations Smoothed estimating function Symmetric distribution |
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