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Estimation in Linear Regression with Laplace Measurement Error Using Tweedie-Type Formula

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Abstract

Based on a Tweedie-type formula developed under the Laplace distribution, this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution. Large sample properties, including the consistency and the asymptotic normality, are investigated. The finite sample performance of the proposed estimators are evaluated via simulation studies, as well as comparison studies with some existing estimation procedures.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041000, China

    Jianhong Shi & Jing Feng

  2. Department of Statistics, Kansas State University, Manhattan, KS, 66503, USA

    Weixing Song

Authors
  1. Jianhong Shi
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  2. Jing Feng
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  3. Weixing Song
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Corresponding authors

Correspondence to Jianhong Shi or Weixing Song.

Additional information

Jianhong Shi’s research is supported by the National Science Foundation of Shanxi Province of China under Grant No. 2013011002-1; Weixing Song’s research is supported by the Division of Mathematical Science, National Science Foundation under Grant No. 1205276.

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Shi, J., Feng, J. & Song, W. Estimation in Linear Regression with Laplace Measurement Error Using Tweedie-Type Formula. J Syst Sci Complex 32, 1211–1230 (2019). https://doi.org/10.1007/s11424-018-7205-x

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  • DOI: https://doi.org/10.1007/s11424-018-7205-x

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