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Self‐Consistent Density Estimation in the Presence of Errors‐in‐Variables

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  • Junhua Zhang
  • Yuping Hu
  • Sanying Feng

Abstract

This paper considers the estimation of the common probability density of independent and identically distributed variables observed with additive measurement errors. The self‐consistent estimator of the density function is constructed when the error distribution is known, and a modification of the self‐consistent estimation is proposed when the error distribution is unknown. The consistency properties of the proposed estimators and the upper bounds of the mean square error and mean integrated square error are investigated under some suitable conditions. Simulation studies are carried out to assess the performance of our proposed method and compare with the usual deconvolution kernel method. Two real datasets are analyzed for further illustration.

Suggested Citation

  • Junhua Zhang & Yuping Hu & Sanying Feng, 2014. "Self‐Consistent Density Estimation in the Presence of Errors‐in‐Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:958702
    DOI: 10.1155/2014/958702
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    References listed on IDEAS

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