Semiparametric efficient estimators in heteroscedastic error models

  • Mijeong KimEmail author
  • Yanyuan Ma


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.


Heteroscedasticity Semiparametric method Standardized regression error Variance function 



Mijeong Kim was supported by a Ewha Womans University Research Grant of 2015 and a National Research Foundation of Korea (NRF) grant funded by the Korean Government (NRF-2017R1C1B5015186). Yanyuan Ma was supported by National Science Foundation DMS-1608540.

Supplementary material

10463_2017_622_MOESM1_ESM.pdf (306 kb)
Supplementary material 1 (pdf 306 KB)


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.Department of StatisticsEwha Womans UniversitySeoulRepublic of Korea
  2. 2.Department of StatisticsPenn State UniversityUniversity ParkUSA

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