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 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
|Date of creation:||11 Aug 2004|
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- 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.
- repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
- 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.
- 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.
- Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
- Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
- Jean-Marc Robin & Richard J. Smith, 2000.
"Tests of rank,"
- 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.
- 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.
- 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.
- J. A. Hausman & W. K. Newey & J. L. Powel, 1988. "Nonlinear Errors in Variables: Estimation of Some Engel Curves," Working papers 504, Massachusetts Institute of Technology (MIT), Department of Economics.
- Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
- 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.
- 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.
- 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.
- Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May.
- Pagan,Adrian & Ullah,Aman, 1999.
Cambridge University Press, number 9780521355643, 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.
- 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.
- Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
- 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.
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