IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i11p3309-3321.html

An application of shrinkage estimation to the nonlinear regression model

Author

Listed:
  • Ahmed, S. Ejaz
  • Nicol, Christopher J.

Abstract

Various large sample estimation techniques in a nonlinear regression model are presented. These estimators are based around preliminary tests of significance, and the James–Stein rule. The properties of these estimators are studied when estimating regression coefficients in the multiple nonlinear regression model when it is a priori suspected that the coefficients may be restricted to a subspace. A simulation based on a demand for money model shows the superiority of the positive-part shrinkage estimator, in terms of standard measures of asymptotic distributional quadratic bias and risk measures, over a range of economically meaningful parameter values. Further work remains in analysing the use of these estimators in economic applications, relative to the inferential approach which is best to use in these circumstances.

Suggested Citation

  • Ahmed, S. Ejaz & Nicol, Christopher J., 2012. "An application of shrinkage estimation to the nonlinear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3309-3321.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3309-3321
    DOI: 10.1016/j.csda.2010.07.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947310003099
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2010.07.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Simon Stevenson, 2001. "Bayes-Stein Estimators and International Real Estate Asset Allocation," Journal of Real Estate Research, American Real Estate Society, vol. 21(1/2), pages 89-104.
    2. Helen X. H. Bao & Alan T. K. Wan, 2007. "Improved Estimators of Hedonic Housing Price Models," Journal of Real Estate Research, American Real Estate Society, vol. 29(3), pages 267-302.
    3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    4. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, vol. 52(4), pages 873-885, July.
    5. Ghosh M. & Saleh A.K.Md.E. & Sen P.K., 1989. "Empirical Bayes Subset Estimation In Regression Models," Statistics & Risk Modeling, De Gruyter, vol. 7(1-2), pages 15-36, February.
    6. Ahmed, S. E. & Saleh, A. K. Md. E., 1990. "Estimation strategies for the intercept vector in a simple linear multivariate normal regression model," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 193-206, December.
    7. White, Kenneth J, 1978. "A General Computer Program for Econometric Methods-Shazam," Econometrica, Econometric Society, vol. 46(1), pages 239-240, January.
    8. Kazimi, Camilla & Brownstone, David, 1999. "Bootstrap confidence bands for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 90(1), pages 99-127, May.
    9. Ahmed, S. E. & Krzanowski, W. J., 2004. "Biased estimation in a simple multivariate regression model," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 689-696, May.
    10. S. K. Sapra, 2003. "Pre-test estimation in Poisson regression model," Applied Economics Letters, Taylor & Francis Journals, vol. 10(9), pages 541-543.
    11. Adkins, Lee C. & Hill, R. Carter, 1989. "Risk characteristics of a stein-like estimator for the probit regression model," Economics Letters, Elsevier, vol. 30(1), pages 19-26.
    12. Knight J. R. & Hill R. Carter & Sirmans C. F., 1993. "Estimation of Hedonic Housing Price Models Using Nonsample Information: A Monte Carlo Study," Journal of Urban Economics, Elsevier, vol. 34(3), pages 319-346, November.
    13. Maddala, G S, et al, 1997. "Estimation of Short-Run and Long-Run Elasticities of Energy Demand from Panel Data Using Shrinkage Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 90-100, January.
    14. Ahmed, S. Ejaz, 1994. "Improved estimation in a multivariate regression model," Computational Statistics & Data Analysis, Elsevier, vol. 17(5), pages 537-554, June.
    15. Dexter, Albert S & Levi, Maurice D & Nault, Barrie R, 1993. "Freely Determined versus Regulated Prices: Implications for the Measured Link between Money and Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(2), pages 222-230, May.
    16. Alan Wan & Anoop Chaturvedi & Guohuazou Zou, 2003. "Unbiased estimation of the MSE matrices of improved estimators in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(2), pages 173-189.
    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. Stephen S. M. Lee & Mehdi Soleymani, 2015. "A Simple Formula for Mixing Estimators With Different Convergence Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1463-1478, December.
    2. Tiefeng Ma & Shuangzhe Liu & S. Ahmed, 2014. "Shrinkage estimation for the mean of the inverse Gaussian population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 733-752, August.
    3. Solomon W. Polachek & Tirthatanmoy Das & Rewat Thamma-Apiroam, 2015. "Micro- and Macroeconomic Implications of Heterogeneity in the Production of Human Capital," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1410-1455.

    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. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
    2. Ahmed, S. E. & Krzanowski, W. J., 2004. "Biased estimation in a simple multivariate regression model," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 689-696, May.
    3. Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
    4. Boris Branisa & Adriana Cardozo, 2009. "Revisiting the Regional Growth Convergence Debate in Colombia Using Income Indicators," Ibero America Institute for Econ. Research (IAI) Discussion Papers 194, Ibero-America Institute for Economic Research, revised 21 Aug 2009.
    5. M. Bagella & L. Becchetti, 1999. "The Determinants of Motion Picture Box Office Performance: Evidence from Movies Produced in Italy," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 23(4), pages 237-256, November.
    6. Godfrey, Leslie G., 1998. "Hausman tests for autocorrelation in the presence of lagged dependent variables Some further results," Journal of Econometrics, Elsevier, vol. 82(2), pages 197-207, February.
    7. Breusch, Trevor & Ward, Michael B. & Nguyen, Hoa Thi Minh & Kompas, Tom, 2011. "On the Fixed-Effects Vector Decomposition," Political Analysis, Cambridge University Press, vol. 19(2), pages 123-134, April.
    8. Anikó Bíró, 2013. "Subjective mortality hazard shocks and the adjustment of consumption expenditures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1379-1408, October.
    9. Zanini, Fabio C. & Irwin, Scott H. & Schnitkey, Gary D. & Sherrick, Bruce J., 2000. "Estimating Farm-Level Yield Distributions For Corn And Soybeans In Illinois," 2000 Annual meeting, July 30-August 2, Tampa, FL 21720, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. Giuseppe Croce & Emanuela Ghignoni, 2011. "Overeducation and spatial flexibility in Italian local labour markets," Working Papers in Public Economics 145, Department of Economics and Law, Sapienza University of Rome.
    11. Chasco, Coro & López, Ana María & Guillain, Rachel, 2008. "The non-stationary influence of geography on the spatial agglomeration of production in the EU," MPRA Paper 10737, University Library of Munich, Germany.
    12. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    13. Caginalp, Gunduz & DeSantis, Mark, 2017. "Does price efficiency increase with trading volume? Evidence of nonlinearity and power laws in ETFs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 436-452.
    14. Jongeneel, Roelof A. & Ge, Lan, 2005. "Explaining Growth in Dutch Agriculture: Prices, Public R&D, and Technological Change," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24573, European Association of Agricultural Economists.
    15. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    16. Kevin J. Fox & Ulrich Kohli & Alice Shiu, 2010. "Trade Agreements and Trade Opportunities: A Flexible Approach for Modeling Australian Export and Import Elasticities," Review of International Economics, Wiley Blackwell, vol. 18(3), pages 513-530, August.
    17. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    18. Hany Eldemerdash & Hugh Metcalf & Sara Maioli, 2014. "Twin deficits: new evidence from a developing (oil vs. non-oil) countries’ perspective," Empirical Economics, Springer, vol. 47(3), pages 825-851, November.
    19. Rao, Surekha & Ghali, Moheb & Krieg, John, 2008. "On the J-test for nonnested hypotheses and Bayesian extension," MPRA Paper 14637, University Library of Munich, Germany.
    20. Agnes Quisumbing & Neha Kumar, 2011. "Does social capital build women's assets? The long-term impacts of group-based and individual dissemination of agricultural technology in Bangladesh," Journal of Development Effectiveness, Taylor & Francis Journals, vol. 3(2), pages 220-242.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:56:y:2012:i:11:p:3309-3321. 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.