A nonparametric hypothesis test via the Bootstrap resampling

Temel, Tugrul (2011): A nonparametric hypothesis test via the Bootstrap resampling.

Abstract

This paper adapts an already existing nonparametric hypothesis test to the bootstrap framework. The test utilizes the nonparametric kernel regression method to estimate a measure of distance between the models stated under the null hypothesis. The bootstraped version of the test allows to approximate errors involved in the asymptotic hypothesis test. The paper also develops a Mathematica Code for the test algorithm.

• Item Type: MPRA Paper
• Language: English
• Keywords: Hypothesis test; the bootstrap; nonparametric regression; omitted variables
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General

References

Andrews, D. W. K., & Buchinsky, M. (2000). A three-step method for choosing the number of bootstrap repetitions. Econometrica, 68(1), 23-51.

Cao-Abad, R. (1991). Rate of convergence for the wild bootstrap in nonparametric regression. The Annals of Statistics, 19(4), 2226-2231.

Delgado, A. M., & Manteiga, G. W. (1999). Signi�cance testing in nonparametric regression based on the bootstrap. Unpublished manuscript. Universidad Carlos III de Madrid and Universidad de Santiago de Compostela.

Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7, 1-26.

Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Philadelphia: Siam Publishing.

Epstein, L.G., & Yatchew, A. J. (1985). Nonparametric hypothesis testing procedures and applications to demand analysis. Journal of Econometrics, 30, 149-169.

Fan, Y., & Li, Q. (1996). Consistent model speci�cation tests: Omitted variables and semiparamtric functional forms. Econometrica, 64(4), 865-890.

Freedman, D. A. (1981). Bootstraping regression models. Annals of Statistics, 9, 1218-1228.

Freedman, D. A. (1984). On bootstraping two-stage least squares in stationary linear models. Annals of Statistics, 12, 827-842.

Giersbergen, N. van. (1998). Bootstraping dynamic econometric models. Unpublished doctoral dissertation, University of Amsterdam, the Netherlands.

Gozalo, L. P. (1993). A consistent model speci�cation test for nonparametric estimation of regression function models. Economic Theory, 9, 451-477.

Hall, P. (1988). On symmetric bootstrap con�dence intervals. Journal of the Royal Statistical Society, Series B, 50, 35-45.

Hall, P., & Hart, J. D. (1990). Bootstrap test for di¤erence between means in nonparametric regression. Journal of the American Statistical Association, 85, 1039-1049.

Hall, P. (1994). Methodology and theory for the bootstrap. In R. F. Engle and D. L. McFadden (Eds.), Handbook of Econometrics: Vol. IV (pp. 2342-2379).

Hall, P., & Horowitz, L. J. (1996). Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica, 64(4), 891-916.

Härdle, W. (1991). Applied Nonoparametric Regression. Cambridge University Press.

Horowitz, L. J., & Härdle, W. (1994). Testing a parametric model against a semiparametric alternative. Economic Theory, 10, 821-848.

Huskova, M., & Janssen, P. (1993). Consistency of the generalized bootstrap for degenerate U-statistics. The Annals of Statistics, 21(4), 1811-1823.

Lavergne, P., & Vuong, Q. H. (1996). Nonparametric selection of regressors: The nonnested case. Econometrica 64(1):207-219.

Lee, A. J. (1990). U-statistics: Theory and practice. New York and Basel: Marcel Dekker, Inc.

Lee, J. B. (1992). A heteroscedasticity test robust to conditional mean misspecification. Econometrica, 60(1), 159-171.

Lewbel, A. (1995). Consistent nonparametric hypothesis tests with an application to Slutsky symmetry. Journal of Econometrics, 67, 379-401.

Li, H., & Maddala, G. S. (1996). Bootstraping time series models. Econometric Reviews, 15, 115-158.

Liu, R. Y., & Singh, K. (1992). Moving blocks jackknife and bootstrap capture week dependence. In R. LePage and L. Billard (Eds.)., Exploring the limit of bootstrap. New York: Wiley.

Mammen, E. (1993). Bootstrap and wild bootstrap for high dimensional linear models. The Annals of Statistics, 21(1), 255-285.

Phillips, P. C. B., & Park, J. Y. (1988). On the formulation of Wald tests of nonlinear restrictions. Econometrica, 56, 1065-1083.

Powell, L. J., Stock, H. J., & Stoker, M. T. (1989). Semiparametric estimation of index coe¢ cients. Econometrica, 57(6), 1403-1430.

Robinson, P.M. (1988). Root-N-consistent semiparametric regression. Econometrica, 56(4), 931-954.

Robinson, P.M. (1989). Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of Economic Studies, 56, 511-534.

Sherman, R. P. (1994). U