IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v142y2008i1p162-182.html
   My bibliography  Save this article

Local rank tests in a multivariate nonparametric relationship

Author

Listed:
  • Fortuna, Natercia

Abstract

Consider a multivariate nonparametric model where the unknown vector of functions depends on two sets of explanatory variables. For a fixed level of one set of explanatory variables, we provide consistent statistical tests, called local rank tests, to determine whether the multivariate relationship can be explained by a smaller number of functions. We also provide estimators for the smallest number of functions, called local rank, explaining the relationship. The local rank tests and the estimators of the local rank are based on the asymptotics of the eigenvalues of some matrix. This matrix is estimated by using kernel-based methods and the asymptotics of its eigenvalues is established by using the so-called Fujikoshi expansions along with some techniques of the theory of U-statistics. We present a simulation study which examines small sample properties of local rank tests. We also apply the local rank tests and the local rank estimators of the paper to a demand system given by a newly constructed data set. Our results can be viewed as localized counterparts of tests for a number of factors in a nonparametric relationship introduced by Donald
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
    • Handle: RePEc:eee:econom:v:142:y:2008:i:1:p:162-182
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(07)00125-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lwebel Arthur & Perraudin William, 1995. "A Theorem on Portfolio Separation with General Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 624-626, April.
    2. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-705, May.
    3. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
    5. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
    6. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
    7. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2011. "Local and Global Rank Tests for Multivariate Varying-Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 295-306.
    8. Russell, Thomas & Farris, Frank, 1993. "The geometric structure of some systems of demand equations," Journal of Mathematical Economics, Elsevier, vol. 22(4), pages 309-325.
    9. Christopher J. Nicol, 2001. "The rank and model specification of demand systems: an empirical analysis using United States microdata," Canadian Journal of Economics, Canadian Economics Association, vol. 34(1), pages 259-289, February.
    10. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(2), pages 151-175, April.
    11. Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995. "Nonlinear errors in variables Estimation of some Engel curves," Journal of Econometrics, Elsevier, vol. 65(1), pages 205-233, January.
    12. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    13. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    14. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    15. Christopher J. Nicol, 2001. "The rank and model specification of demand systems: an empirical analysis using United States microdata," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 34(1), pages 259-289, February.
    16. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(2), pages 222-240, April.
    17. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
    18. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    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. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
    2. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2011. "Local and Global Rank Tests for Multivariate Varying-Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 295-306.
    3. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.

    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. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2011. "Local and Global Rank Tests for Multivariate Varying-Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 295-306.
    2. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.
    3. Panayiota Lyssiotou, 2003. "On estimating the cost of characteristics indices from consumer demand analysis," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(2), pages 326-349, May.
    4. Arthur Lewbel, 2003. "A rational rank four demand system," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 127-135.
    5. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.
    6. Gonzalo Camba-Mendez & George Kapetanios, 2005. "Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling," Working Papers 541, Queen Mary University of London, School of Economics and Finance.
    7. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    8. Takashi Unayama, 2006. "The Engel curve for alcohol and the rank of demand systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1019-1038, November.
    9. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    10. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    11. Anyck Dauphin & Abdel‐Rahmen El Lahga & Bernard Fortin & Guy Lacroix, 2011. "Are Children Decision‐Makers within the Household?," Economic Journal, Royal Economic Society, vol. 121(553), pages 871-903, June.
    12. Inoue, Atsushi & Rossi, Barbara, 2011. "Testing for weak identification in possibly nonlinear models," Journal of Econometrics, Elsevier, vol. 161(2), pages 246-261, April.
    13. Miguel Cabello, 2022. "Robust Estimation of the non-Gaussian Dimension in Structural Linear Models," Papers 2212.07263, arXiv.org, revised Sep 2023.
    14. GUO-FITOUSSI, Liang, 2013. "A Comparison of the Finite Sample Properties of Selection Rules of Factor Numbers in Large Datasets," MPRA Paper 50005, University Library of Munich, Germany.
    15. Dauphin, Anyck & El Lahga, Abdel-Rahmen & Fortin, Bernard & Lacroix, Guy, 2006. "Choix de consommation des ménages en présence de plusieurs décideurs," L'Actualité Economique, Société Canadienne de Science Economique, vol. 82(1), pages 87-118, mars-juin.
    16. Thomas F. Crossley & Hamish W. Low, 2005. "Unexploited Connections Between Intra- and Inter-temporal Allocation," Social and Economic Dimensions of an Aging Population Research Papers 131, McMaster University.
    17. Caglayan, Mustafa & Jehan, Zainab & Mouratidis, Kostas, 2012. "Asymmetric monetary policy rules for open economies: Evidence from four countries," MPRA Paper 37401, University Library of Munich, Germany.
    18. Kemal Bagzibagli, 2014. "Monetary transmission mechanism and time variation in the Euro area," Empirical Economics, Springer, vol. 47(3), pages 781-823, November.
    19. Forchini, Giovanni, 2008. "A characterization of invariant tests for identification in linear structural equations," Economics Letters, Elsevier, vol. 98(2), pages 185-193, February.
    20. LaFrance, Jeffrey T., 2008. "The structure of US food demand," Journal of Econometrics, Elsevier, vol. 147(2), pages 336-349, December.

    More about this item

    JEL classification:

    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    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:econom:v:142:y:2008:i:1:p:162-182. 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/jeconom .

    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.