IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i9p4253-4271.html
   My bibliography  Save this article

On the estimation of the general parameter

Author

Listed:
  • Stearns, Matthew
  • Singh, Sarjinder

Abstract

In this paper, we first discuss the origin, developments and various thoughts by several researchers on the generalized linear regression estimator (GREG) due to Deville and Särndal [Deville, J.C., Särndal, C.E., 1992. Calibration estimators in survey sampling. J. Amer. Statist. Assoc. 87, 376-382]. Then, the problem of estimation of the general parameter of interest considered by Rao [Rao, J.N.K., 1994. Estimating totals and distribution functions using auxiliary information at the estimation stage. J. Official Statist. 10 (2), 153-165], and Singh [Singh, S., 2001. Generalized calibration approach for estimating the variance in survey sampling. Ann. Inst. Statist. Math. 53 (2), 404-417; Singh, S., 2004. Golden and Silver Jubilee Year-2003 of the linear regression estimators. In: Proceedings of the Joint Statistical Meeting, Toronto (Available on the CD), 4382-4380; Singh, S., 2006. Survey statisticians celebrate Golden Jubilee Year-2003 of the linear regression estimator. Metrika 1-18] is further investigated. In addition to that it is shown that the Farrell and Singh [Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] estimators are also a special case of the proposed methodology. Interestingly, it has been noted that the single model assisted calibration constraint studied by Farrell and Singh [Farrell, P.J., Singh, S., 2002. Re-calibration of higher order calibration weights. Presented at Statistical Society of Canada conference, Hamilton (Available on CD); Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] and Wu [Wu, C., 2003. Optimal calibration estimators in survey sampling. Biometrika 90, 937-951] is not helpful for calibrating the Sen [Sen, A.R., 1953. On the estimate of the variance in sampling with varying probabilities. J. Indian Soc. Agril. Statist. 5, 119-127] and Yates and Grundy [Yates, F., Grundy, P.M., 1953. Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. Ser. 15, 253-261] estimator of the variance of the linear regression estimator under the optimal designs of Godambe and Joshi [Godambe, V.P., Joshi, V.M., 1965. Admissibility and Bayes estimation in sampling finite populations--I. Ann. Math. Statist. 36, 1707-1722]. Three new estimators of the variance of the proposed linear regression type estimator of the general parameters of interest are introduced and compared with each other. The newly proposed two-dimensional linear regression models are found to be useful, unlike a simulation based on a couple of thousands of random samples, in comparing the estimators of variance. The use of knowledge of the model parameters in assisting the estimators of variance has been found to be beneficial. The most attractive feature is that it has been shown theoretically that the proposed method of calibration always remains more efficient than the GREG estimator.

Suggested Citation

  • Stearns, Matthew & Singh, Sarjinder, 2008. "On the estimation of the general parameter," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4253-4271, May.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4253-4271
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00056-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sarjinder Singh, 2001. "Generalized Calibration Approach for Estimating Variance in Survey Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 404-417, June.
    2. Sarjinder Singh, 2006. "Survey statisticians celebrate golden jubilee year 2003 of the linear regression estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(1), pages 1-18, February.
    3. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    4. Changbao Wu, 2003. "Optimal calibration estimators in survey sampling," Biometrika, Biometrika Trust, vol. 90(4), pages 937-951, December.
    5. Sitter R.R. & Wu C., 2002. "Efficient Estimation of Quadratic Finite Population Functions in the Presence of Auxiliary Information," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 535-543, June.
    6. Rueda, M. & Martinez, S. & Martinez, H. & Arcos, A., 2006. "Mean estimation with calibration techniques in presence of missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3263-3277, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martínez, S. & Rueda, M. & Arcos, A. & Martínez, H. & Sánchez-Borrego, I., 2011. "Post-stratified calibration method for estimating quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 838-851, January.
    2. Sarjinder Singh, 2012. "On the calibration of design weights using a displacement function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 85-107, January.
    3. Ohyama, Tetsuji, 2013. "Prior value incorporated calibration estimator in stratified random sampling," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 46-51.
    4. Al-Jararha J. & Sulaiman Mazen, 2020. "Horvitz-Thompson estimator based on theauxiliary variable," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 37-54, March.
    5. J. Al-Jararha & Mazen Sulaiman, 2020. "Horvitz-Thompson estimator based on the auxiliary variable," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 37-53, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kim, Jong-Min & Sungur, Engin A. & Heo, Tae-Young, 2007. "Calibration approach estimators in stratified sampling," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 99-103, January.
    2. Changbao Wu & Shixiao Zhang, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1082-1086, December.
    3. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Moreno-Rebollo, J.L. & Muñoz-Pichardo, J.M., 2012. "Case-deletion type diagnostics for calibration estimators in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2219-2236.
    4. Aylin Alkaya & H. Öztaş Ayhan & Alptekin Esin, 2017. "Sequential Data Weighting Procedures For Combined Ratio Estimators In Complex Sample Surveys," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 247-270, June.
    5. Zhan Liu & Chaofeng Tu & Yingli Pan, 2022. "Model-assisted calibration with SCAD to estimated control for non-probability samples," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 849-879, October.
    6. Alkaya Aylin & Ayhan H. Öztaş & Esin Alptekin, 2017. "Sequential Data Weighting Procedures for Combined Ratio Estimators in Complex Sample Surveys," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 247-270, June.
    7. Maria del Mar Rueda, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1077-1081, December.
    8. Rueda, M. & Martinez, S. & Martinez, H. & Arcos, A., 2006. "Mean estimation with calibration techniques in presence of missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3263-3277, July.
    9. Jason P. Estes & Bhramar Mukherjee & Jeremy M. G. Taylor, 2018. "Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 568-586, December.
    10. Martínez, S. & Rueda, M. & Arcos, A. & Martínez, H. & Sánchez-Borrego, I., 2011. "Post-stratified calibration method for estimating quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 838-851, January.
    11. Debashis Ghosh & Michael S. Sabel, 2022. "A Weighted Sample Framework to Incorporate External Calculators for Risk Modeling," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 363-379, December.
    12. Domingo Morales & María del Mar Rueda & Dolores Esteban, 2018. "Model-Assisted Estimation of Small Area Poverty Measures: An Application within the Valencia Region in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 873-900, August.
    13. Ieva Burakauskaitė & Andrius Čiginas, 2023. "An Approach to Integrating a Non-Probability Sample in the Population Census," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    14. M. Rueda & I. Sánchez-Borrego & A. Arcos & S. Martínez, 2010. "Model-calibration estimation of the distribution function using nonparametric regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 33-44, January.
    15. Xiaogang Duan & Guosheng Yin, 2017. "Ensemble Approaches to Estimating the Population Mean with Missing Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 899-917, December.
    16. Denis Devaud & Yves Tillé, 2019. "Deville and Särndal’s calibration: revisiting a 25-years-old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1033-1065, December.
    17. Wang, Qihua & Lai, Peng, 2011. "Empirical likelihood calibration estimation for the median treatment difference in observational studies," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1596-1609, April.
    18. A. Arcos & M. Rueda & M. Martínez-Miranda, 2005. "Using multiparametric auxiliary information at the estimation stage," Statistical Papers, Springer, vol. 46(3), pages 339-358, July.
    19. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    20. Jan Pablo Burgard & Ralf Münnich & Martin Rupp, 2019. "A Generalized Calibration Approach Ensuring Coherent Estimates with Small Area Constraints," Research Papers in Economics 2019-10, University of Trier, Department of Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4253-4271. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.