Skip to main content
SpringerLink
Log in

Model-calibration estimation of the distribution function using nonparametric regression

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Nonparametric regression has only recently been employed in the estimation of finite population parameters in a model-assisted framework. This paper proposes a new calibration estimator for the distribution function using nonparametric methods to obtain the fitted values on which to calibrate. The proposed estimator is a genuine distribution function that presents several attractive features. In terms of relative efficiency and relative bias, the behaviour of the proposed estimator is compared to other known estimators in a limited simulation study on real populations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

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 

  • Breidt FJ, Opsomer JD, Johnson AA, Ranalli MG (2007) Semiparametric model-assisted estimation for natural resource surveys. Surv Methodol 33: 35–44

    Google Scholar 

  • Chambers RL, Dunstan R (1986) Estimating distribution functions from survey data. Biometrika 73: 597–604

    Article  MATH  MathSciNet  Google Scholar 

  • Chen J, Wu C (2002) Estimation of distribution function and quantiles using the model-calibrated pseudo empirical likelihood method. Stat Sin 12: 1223–1239

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

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Francisco CA, Fuller WA (1991) Quantile estimation with a complex survey design. Ann Stat 19(1): 454–469

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman JH (1991) Multivariate adaptive regression splines, with discussion. Ann Stat 19: 1–67

    Article  MATH  Google Scholar 

  • Johnson AA, Breidt FJ, Opsomer JD (2004) Estimating distribution functions from survey data using nonparametric regression. Preprint series #04-07. Department of Statistics, Iowa State University. J Stat Theory Pract (to appear)

  • Kuk A, Mak TK (1989) Median estimation in the presence of auxiliary information. J R Stat Soc B 51(2): 261–269

    MATH  MathSciNet  Google Scholar 

  • Kuk A, Mak TK (1994) A functional approach to estimating finite population distribution functions. Commun Stat Theory Meth 23(3): 883–896

    Article  MATH  MathSciNet  Google Scholar 

  • Kuo L (1988) Classical and prediction approaches to estimating distribution functions from survey data. In: American statistical association, Proceedings of the section on survey research methods pp 280–2854

  • Montanari GE, Ranalli MG (2005a) Nonparametric model calibration estimation in survey sampling. J Am Stat Assoc 100: 1429–1442

    Article  MATH  MathSciNet  Google Scholar 

  • Montanari GE, Ranalli MG (2005b) Nonparametric methods for sample surveys of environmental populations, available at http://cab.unime.it/mus/arvhive/00000363/

  • Murthy MN (1967) Sampling theory and method. Statistical Publishing Society, Calcutta

    Google Scholar 

  • Nadaraya EA (1964) On estimating regression. Theory Probab Appl 15: 134–137

    Article  Google Scholar 

  • Rao JNK, Kovar JG, Mantel HJ (1990) On estimating distribution fucntions and quantiles from survey data using auxiliary information. Biometrika 77: 365–375

    Article  MATH  MathSciNet  Google Scholar 

  • Ruppert D, Wand MP (1994) Multivariate locally weighted least squares regression. Ann Stat 22(3): 1346–1370

    Article  MATH  MathSciNet  Google Scholar 

  • Rueda M, Martínez S, Martínez H, Arcos A (2007) Estimation of the distribution function with calibration methods. J Stat Plan Inference 137(2): 435–448

    Article  MATH  Google Scholar 

  • Särndal C (2007) The calibration approach in survey theory and practice. Surv Methodol 33(2): 99–119

    Google Scholar 

  • Särndal CE, Swensson B, Wretman (1992) Model assisted survey sampling. Springer, Heidelberg

    MATH  Google Scholar 

  • Silva PLD, Skinner CJ (1995) Estimation distribution functions with auxiliary information using poststratification. J Off Stat 11(3): 277–294

    Google Scholar 

  • Singh S (2001) Generalized calibration approach for estimating variance in survey sampling. Ann Inst Stat Math 53(2): 404–417

    Article  MATH  Google Scholar 

  • Singh S (2006) Golden and silver jubilee year 2003 of the linear regression estimators. Metrika 63(1): 1–18

    Article  MATH  MathSciNet  Google Scholar 

  • Singh S, Horn S, Tracy DS (2001) Hybrid of calibration and imputation: estimation of mean in survey sampling. Statistica LXI(1): 27–41

    MathSciNet  Google Scholar 

  • Wang S, Dorfman AH (1996) A new estimator for the finite population distribution function. Biometrika 83: 639–652

    Article  MATH  MathSciNet  Google Scholar 

  • Watson GS (1964) Smooth regression analysis. Sankhya Ser A 26: 359–372

    MATH  MathSciNet  Google Scholar 

  • Wu C (2003) Optimal calibration estimators in surveys sampling. Biometrika 90: 937–951

    Article  MathSciNet  Google Scholar 

  • Wu C, Sitter RR (2001) A model-calibration approach to using complete auxiliary information from survey data. J Am Stat Assoc 96: 185–193

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Operational Research, University of Granada, 18071, Granada, Spain

    M. Rueda, I. Sánchez-Borrego & A. Arcos

  2. Department of Statistics and Applied Mathematics, University of Almería, 04071, Almería, Spain

    S. Martínez

Authors
  1. M. Rueda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Sánchez-Borrego
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Arcos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Martínez
    View author publications

    You can also search for this author in PubMed 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., Arcos, A. et al. Model-calibration estimation of the distribution function using nonparametric regression. Metrika 71, 33–44 (2010). https://doi.org/10.1007/s00184-008-0199-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-008-0199-y

Keywords

Search

Navigation