Finite Population Model-Assisted Estimation Using Combined Parametric and Nonparametric Regression Smoothers

  • Sayed A. MostafaEmail author
  • Qingsong Shan
Original Article
Part of the following topical collections:
  1. Algorithms, Analysis and Advanced Methodologies in the Design of Experiments


This paper considers estimating finite population totals from complex sample surveys in the presence of auxiliary information. Model-assisted estimators which assume a working regression model relating the study variable with the auxiliary data are common in this context. Both parametric and nonparametric working models have been utilized individually in constructing several model-assisted estimators. Model-assisted estimators with parametric working models are known to be efficient when the assumed working model is correctly specified, while using nonparametric smoothers gives more robust estimates but requires relatively large sample sizes. In this paper, we consider the situation where the researcher has an idea of which parametric model can describe the relationship between the study variable and the auxiliary data, but this model may not be adequate in some areas of the data range. Using combined parametric and nonparametric regression smoothers for the working model, we introduce a new class of model-assisted estimators for finite population totals. The proposed estimators are shown to have the desirable asymptotic properties of traditional model-assisted estimators of population totals. The finite sample performance of the new estimators is studied via Monte Carlo simulations from both artificial and real populations. The empirical results suggest that our proposed estimators perform well relative to other model-based and model-assisted estimators as well as the customary Horvitz–Thompson estimator under different levels of misspecification in the working model. We also discuss the problem of variance estimation for the proposed estimators.


Model-assisted estimation Combined smoothers Complex surveys Nonparametric regression 

Mathematics Subject Classification

62D05 62G08 



The authors are indebted to the Editor and three anonymous referees for their insightful suggestions that led to improving this paper substantially.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Breidt FJ, Claeskens G, Opsomer JD (2005) Model-assisted estimation for complex surveys using penalised splines. Biometrika 92:831–846MathSciNetCrossRefGoogle Scholar
  2. 2.
    Breidt JF, Opsomer JD (2000) Local polynomial regression estimators in survey sampling. Ann Stat 28:1026–1053CrossRefGoogle Scholar
  3. 3.
    Breidt JF, Opsomer JD (2017) Model-assisted survey estimation with modern prediction techniques. Stat Sci 32:190–205MathSciNetCrossRefGoogle Scholar
  4. 4.
    Burman P, Chaudhuri P (1994) A hybrid approach to parametric and nonparametric regression. Technical Report No. 243, Division of Statistics, University of Califronia, DavisGoogle Scholar
  5. 5.
    Burman P, Chaudhuri P (2011) On a hybrid approach to parametric and nonparametric regression. In: Nonparametric statistical methods and related topics: AFestschrift in Honor of Professor P. K. Bhattacharya on the Occasion of his 80th Birthday, pp 233–256CrossRefGoogle Scholar
  6. 6.
    CDE (2018) Academic performance index (API). Accessed 30 Jun 2019
  7. 7.
    Dorfman AH (1992) Non-parametric regression for estimating totals in finite populations. In: ASA proceedings of the section on survey research methods. American Statistical Association (Alexandria, VA), pp 622–625Google Scholar
  8. 8.
    Glad IK (1998) Nonparametric correction of parametric regression estimates. Scand J Stat 25:649–668MathSciNetCrossRefGoogle Scholar
  9. 9.
    Harms T, Duchesne P (2010) On kernel nonparametric regression designed for complex survey data. Metrika 72:111–138MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mays JE, Birch JB, Starnes A (2001) Model robust regression: combining parametric, nonparametric, and semiparametric methods. J Nonparametric Stat 13(2):245–277MathSciNetCrossRefGoogle Scholar
  11. 11.
    Montanari GE, Ranalli MG (2005) Nonparametric methods in survey sampling. In: Bock HH et al (eds) New developments in classification and data analysis. Studies in classification, data analysis and knowledge organization. Springer, Berlin, pp 203–210CrossRefGoogle Scholar
  12. 12.
    R Core Team (2017) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  13. 13.
    Rahman M, Ullah A (2002) Improved combined parametric and nonparametric regressions: estimation and hypothesis testing. Handb Appl Econ Stat Inference 165:158–175MathSciNetGoogle Scholar
  14. 14.
    Robinson PM, Särndal CE (1983) Asymptotic properties of the generalized regression estimator in probability sampling. Sankhya Ser B 45:240–248MathSciNetzbMATHGoogle Scholar
  15. 15.
    Rondon LM, Vanegas LH, Ferraz C (2012) Finite population estimation under generalized linear model assistance. Comput Stat Data Anal 56:680–697MathSciNetCrossRefGoogle Scholar
  16. 16.
    Särndal CE, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, New YorkCrossRefGoogle Scholar
  17. 17.
    Ullah A, Vinod HD (1993) General nonparametric regression estimation and testing in econometrics. Handb Stat 11:85–117MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wu C, Sitter RR (2001) A model-calibration approach to using complete auxiliary information from survey data. J Am Stat Assoc 96:185–193MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhang G, Christensen F, Zheng W (2015) Nonparametric regression estimators in complex surveys. J Stat Comput Simul 85:1026–1034MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsNorth Carolina A&T State UniversityGreensboroUSA
  2. 2.Department of StatisticsJiangxi University of Finance and EconomicsNanchangChina

Personalised recommendations