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Semiparametric efficient estimators in heteroscedastic error models

Author

Listed:
  • Mijeong Kim

    (Ewha Womans University)

  • Yanyuan Ma

    (Penn State University)

Abstract

In the mean regression context, this study considers several frequently encountered heteroscedastic error models where the regression mean and variance functions are specified up to certain parameters. An important point we note through a series of analyses is that different assumptions on standardized regression errors yield quite different efficiency bounds for the corresponding estimators. Consequently, all aspects of the assumptions need to be specifically taken into account in constructing their corresponding efficient estimators. This study clarifies the relation between the regression error assumptions and their, respectively, efficiency bounds under the general regression framework with heteroscedastic errors. Our simulation results support our findings; we carry out a real data analysis using the proposed methods where the Cobb–Douglas cost model is the regression mean.

Suggested Citation

  • Mijeong Kim & Yanyuan Ma, 2019. "Semiparametric efficient estimators in heteroscedastic error models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 1-28, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0622-0
    DOI: 10.1007/s10463-017-0622-0
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    References listed on IDEAS

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    1. Heng Lian & Hua Liang & Raymond J. Carroll, 2015. "Variance function partially linear single-index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 171-194, January.
    2. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    3. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    4. Mijeong Kim & Yanyuan Ma, 2012. "The efficiency of the second-order nonlinear least squares estimator and its extension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 751-764, August.
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