Skip to main content
Log in

Model-based variance estimation under unequal probability sampling

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

This paper deals with a model-based variance estimation of the Horvitz–Thompson (HT) estimator when auxiliary information is available. A small simulation study is carried out to illustrate and establish some of the findings.

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

Access this article

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

  • Berger YG (1998) Variance estimation using list sequential scheme for unequal probability sampling. J Official Stat 14(3):315–323

    Google Scholar 

  • Brewer KRW (1963) Ratio estimation and finite population: some results deductible from the assumption of an underlying stochastic process. Aust J Stat 5:93–105

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Chen J, Sitter RR (1999) A pseudo empirical likelihood approach to the effective use of auxiliary information in complex surveys. Stat Sin 9:385–406

    MATH  MathSciNet  Google Scholar 

  • Deng LY, Wu CFJ (1987) Estimation of the regression estimator. J Am Stat Assoc 82:568–576

    Article  MATH  MathSciNet  Google Scholar 

  • Deville JC, Särndal CE (1992) Calibration using auxiliary information. J Am Stat Assoc 78:117–123

    Google Scholar 

  • Foreman EK (1991) Survey sampling principles. Marcel Dekker, Inc., New York

    MATH  Google Scholar 

  • Fuller WA (1970) Sampling with random stratum boundrties. J R Stat Soc B 32:209–226

    MATH  MathSciNet  Google Scholar 

  • Hanif M, Brewer KRW (1980) Sampling with unequal probabilities without replacement: a review. Int Stat Rev 48:317–335

    MATH  MathSciNet  Google Scholar 

  • Hanif M, Mukhopadhyay P, Bhattacharyya S (1993) On estimating the variance of Horvitz- Thompson estimator. Pakistan J Stat 81A:123–136

    MathSciNet  Google Scholar 

  • Hedayat AS, Sinha BK (1991) Design and Inference in finite population sampling. Wiley, New York

    MATH  Google Scholar 

  • Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47:663–685

    Article  MATH  MathSciNet  Google Scholar 

  • Isaki CT (1983) Variance estimation using auxiliary information. J Am Stat Assoc 78(381):117–123

    Article  MATH  MathSciNet  Google Scholar 

  • Kish L (1965) Survey sampling. Wiley, New York

    MATH  Google Scholar 

  • Kuk AYC (1989) Double bootstrap estimation of variance under systematic sampling with probability proportional to size. J Stat Computation Simulation 31:78–82

    MathSciNet  Google Scholar 

  • Kumar P, Gupta VK, Agarwal S (1985) On variance estimation in unequal probability sampling. Aust J Stat 27(2):197–201

    Google Scholar 

  • Liu TP (1974) A general unbiased estimator for the variance of finite population. Sankhya Ser C 36:23–32

    MATH  Google Scholar 

  • Liu TP, Thompson DJ (1983) Properties of estimators of quadratic finite population functions: the batch approach. Ann Stat 11:275–285

    Article  MATH  MathSciNet  Google Scholar 

  • Midzuno H (1952) On the sampling system with probabilities proportional to sum of sizes. Ann Inst Stat Math 3:99–107

    Article  MATH  MathSciNet  Google Scholar 

  • Muirhead RJ (1982) Aspects of multivariate statistical theory. Wiley, New York

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Royall RM, Cumberland WG (1978) Variance estimation in finite population sampling. J Am Stat Assoc 73:351–358

    Article  MathSciNet  Google Scholar 

  • Royall RM, Cumberland WG (1981a) An empirical study of the ratio estimator and estimators of its variance. J Am Stat Assoc 76:66–88

    Article  MATH  MathSciNet  Google Scholar 

  • Royall RM, Cumberland WG (1981b) The finite population linear regression estimator and estimators of its variance- An empirical study. J Am Stat Assoc 76:924–930

    Article  MathSciNet  Google Scholar 

  • Royall RM, Eberhardt KR (1975) Variance estimates for the ratio estimator. Sankhya Ser 37:43–52

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Seber GAF (1984) Multivariate observations. John Wiley, New York

    MATH  Google Scholar 

  • Shah DN, Patel PA (1994) Optimum estimation for a finite population variance under certain super-population model. J Indian Stat Assoc 32(1):21–28

    MathSciNet  Google Scholar 

  • Shah DN, Patel PA (1996) Asymptotic properties of a generalized regression-type predictor of a finite population variance in probability sampling. Can J Stat 24(3):373–384

    Article  MATH  MathSciNet  Google Scholar 

  • Singh S, Horn S, Chowdhury S, Yu S (1999) Calibration of the estimators of variance. Aust N Z J Stat 41:199–212

    Article  MATH  MathSciNet  Google Scholar 

  • Sitter RR, Wu C (2002) Efficient estimation of quadratic finite population functions in the presence of auxiliary information. J Am Stat Assoc 97:535–543

    Article  MATH  MathSciNet  Google Scholar 

  • Stehman SV, Overton WS (1994) Comparison of variance estimators of the Horvitz-Thompson estimator for randomized variable probability systematic sampling. J Am Stat Assoc 89:30–43

    Article  MATH  Google Scholar 

  • Sukhatme PV, Sukhatme BV (1970) Sampling theory of survey with application, 2nd edn. Asia Publishing House, London

    Google Scholar 

  • Sunter AB (1977a) Response burden, sample rotation, and classification renewal in economic surveys. Int Stat Rev 45:209–222

    Article  Google Scholar 

  • Sunter AB (1977b) List Sequential sampling with equal or unequal probabilities without replacement. Appl Stat 26:261–268

    Article  MathSciNet  Google Scholar 

  • Valliant R, Dorfman AH, Royall RM (2000) Finite population sampling and inference. Wiley, New York

    MATH  Google Scholar 

  • Wolter KM (1985) Introduction to variance estimation. Springer Verlag, New York

    MATH  Google Scholar 

  • Wu CFJ, Deng LY (1983) Estimation of variance of the ratio estimator: an empirical study. In: Scientific inference data analysis and robustness, pp 245–277

  • Wu C, Sitter RR (2001) Variance estimation for the finite population distribution function with complete auxiliary information. Can J Stat 29:289–307

    Article  MATH  MathSciNet  Google Scholar 

  • Yates F (1960) Sampling Methods for censuses and surveys, 3rd edn. Hafner Publishing Company, New York

    Google Scholar 

  • Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. J R Stat Soc B 15:235–261

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. D. Chaudhari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Patel, P.A., Chaudhari, R.D. Model-based variance estimation under unequal probability sampling. Metrika 67, 171–187 (2008). https://doi.org/10.1007/s00184-007-0128-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0128-5

Keywords

Navigation