Skip to main content
Springer Nature Link
Log in

A predictive estimator of finite population mean using nonparametric regression

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

The paper considers the problem of estimating the population mean using auxiliary information. We propose a new model-based estimator of the population mean, based on local polynomial regression. This estimator exhibits several attractive properties under the model-based approach. The estimator is compared to a number of methods which have been proposed in the literature via a simulation study based on several populations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Breidt FJ, Opsomer JD (2000) Local polynomial regression estimators in survey sampling. Ann Stat 28(4): 1026–1053

    Article  MATH  MathSciNet  Google Scholar 

  • Cassell CM, Sarndal CE, Wretman JH (1977) Foundations of inference in survey sampling. Wiley, New York

    Google Scholar 

  • Chambers RL, Dorfman AH, Wherly TE (1993) Bias robust estimation in finite populations using nonparametric calibration. J Am Stat Assoc 88: 268–277

    Article  MATH  Google Scholar 

  • Chen J, Qin J (1993) Empirical likelihood estimation for finite populations and the effective usage of auxiliary information. Biometrika 80: 107–116

    Article  MATH  MathSciNet  Google Scholar 

  • Deville JC, Särndal CE (1992) Calibration estimators in survey sampling. J Am Stat Assoc 87: 376–382

    Article  MATH  Google Scholar 

  • Dorfman AH (1993) A comparison of design-based and model-based estimators of the finite population distribution function. Aust J Stat 35: 29–41

    Article  MATH  MathSciNet  Google Scholar 

  • Dorfman AH, Hall P (1993) Estimators of the finite population distribution function using nonparametric regression. Ann Stat 16(3): 1452–1475

    Article  MathSciNet  Google Scholar 

  • Fan J, Gijbels I (1995) Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J R Stat Soc Ser B 59(2): 371–394

    MathSciNet  Google Scholar 

  • Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Chapman and Hall, London

    MATH  Google Scholar 

  • Fox J (1997) Applied regression analysis, linear models and related methods. Sage Publications, McMaster University, Hamilton, Ontario, Canada

  • Godambe VP (1955) A unified theory of sampling from finite populations. J R Stat Soc Ser B 17: 269–278

    MATH  MathSciNet  Google Scholar 

  • Kott PS (2005) Randomization-assisted model-based survey sampling. J Stat Plann Inference 129: 263–277

    Article  MATH  MathSciNet  Google Scholar 

  • Kuk AYC, Welsh AH (2001) Robust estimation for finite populations based on a working model. J R Stat Soc Ser B 63: 277–292

    Article  MATH  MathSciNet  Google Scholar 

  • Kuo L (1988) Classical and prediction approaches to estimating distribution functions from survey data. In: Proceeding of the section on survey researh methods. American Statistical Association, pp 280–285

  • Little RJ (2004) To model or not to model? Competing modes of inference for finite population sampling. J Am Stat Assoc 99(446): 546–556

    Article  MATH  MathSciNet  Google Scholar 

  • Neyman J (1934) On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J R Stat Soc Ser A 97: 558–606

    Article  Google Scholar 

  • Opsomer JD, Miller CP (2005) Selecting the amount of smoothing in nonparametric regression estimation for complex surveys. Nonparametric Stat 17(1): 593–611

    Article  MATH  MathSciNet  Google Scholar 

  • Pineo PC, Porter J, McRoberts HA (1977) The 1971 census and the socioeconomic misclassification of occupations. Can Rev Sociol Anthropol 14: 147–157

    Google Scholar 

  • Royal RM, Cumberland WG (1981) An empirical study of the ratio estimator and estimators of its variance. J Am Stat Assoc 76: 66–77

    Article  Google Scholar 

  • Särndall CE, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, New York

    Google Scholar 

  • Seifert B, Gasser T (2000) Data adaptive ridging in local polynomial regression. J Comput Stat 9: 338–360

    Article  MathSciNet  Google Scholar 

  • Singh S (2003) Advanced sampling theory with applications: How Michael “selected” Amy. Kluwer Academic Publisher, The Netherlands, pp 1–1247

    MATH  Google Scholar 

  • Valliant R, Dorfman AH, Royall RM (2000) Finite population sampling and inference: a prediction approach. Wiley series in probability and statistics, survey methodology section. Wiley, New York

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Operational Research, University of Granada, Granada, Spain

    M. Rueda & I. R. Sánchez-Borrego

Authors
  1. M. Rueda
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. I. R. Sánchez-Borrego
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to M. Rueda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rueda, M., Sánchez-Borrego, I.R. A predictive estimator of finite population mean using nonparametric regression. Comput Stat 24, 1–14 (2009). https://doi.org/10.1007/s00180-008-0140-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-008-0140-x

Keywords