Local rank tests in a multivariate nonparametric relationship
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 local rank are defined in terms of the eigenvalues of a kernel-based estimator of some matrix. The asymptotics of the eigenvalues is established by using the so-called Fujikoshi expansion along with some techniques of the theory of U-statistics. We present a simulation study which examines the small sample properties of local rank tests. We also apply the local rank tests and the local rank estimators to a demand system given by a newly constructed data set. This work can be viewed as a “local” extension of the tests for a number of factors in a nonparametric relationship introduced by Stephen Donald.
|Date of creation:||Feb 2004|
|Date of revision:|
|Contact details of provider:|| Postal: Rua Dr. Roberto Frias, 4200 PORTO|
Web page: http://www.fep.up.pt/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
- Natércia Fortuna, 2004.
"Local rank tests in a multivariate nonparametric relationship,"
FEP Working Papers
137, Universidade do Porto, Faculdade de Economia do Porto.
- Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
- Natercia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," Econometric Society 2004 North American Summer Meetings 446, Econometric Society.
- Robin, Jean-Marc & Smith, Richard J., 2000.
"Tests Of Rank,"
Cambridge University Press, vol. 16(02), pages 151-175, April.
- 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.
- Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
- Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
- Pagan,Adrian & Ullah,Aman, 1999.
Cambridge University Press, number 9780521355643, 1.
- 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.
- 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.
- Donald, Stephen G. & Fortuna, NatÃ©rcia & 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.
- Stephen G. Donald & Natércia Fortuna & Vladas Pipiras, 2005. "Local and global rank tests for multivariate varying-coefficient models," FEP Working Papers 196, Universidade do Porto, Faculdade de Economia do Porto.
- 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.
- 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.
- repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
- Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
- J. A. Hausman & W. K. Newey & J. L. Powel, 1988.
"Nonlinear Errors in Variables: Estimation of Some Engel Curves,"
504, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May.
- 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.
When requesting a correction, please mention this item's handle: RePEc:por:fepwps:137. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.