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Consistent specification testing for conditional moment restrictions. (English) Zbl 1028.62030
This paper introduces specification tests for conditional moment restrictions. The proposed tests are generalizations of the Kolmogorov-Smirnov and Cramér-von Mises tests and are consistent against all alternatives to the null hypothesis, powerful against $$1/n$$ local alternatives and not dependent on any smoothing parameter. A nonparametric bootstrap procedure based on a recentered criterion function is suggested to obtain critical values for the tests and is justified asymptotically.

##### MSC:
 62G10 Nonparametric hypothesis testing 62G09 Nonparametric statistical resampling methods
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##### References:
 [1] Ait-Sahalia, Y.; Bickel, P.J.; Stoker, T.M., (), unpublished manuscript [2] Andrews, D.W.K., A conditional Kolmogorov test, Econometrica, 65, 1097-1128, (1997) · Zbl 0928.62019 [3] Bierens, H.J., Consistent model specification tests, Journal of econometrics, 20, 105-134, (1982) · Zbl 0549.62076 [4] Bierens, H.J., A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458, (1990) · Zbl 0737.62058 [5] Bierens, H.J.; Ploberger, W., Asymptotic theory of integrated conditional moment tests, Econometrica, 65, 1129-1151, (1997) · Zbl 0927.62085 [6] De Jong, R.M., The bierens test under data dependence, Journal of econometrics, 72, 1-32, (1996) · Zbl 0855.62073 [7] Eubank, R.; Spiegelman, S., Testing the goodness of fit of a linear model via nonparametric regression techniques, Journal of the American statistical association, 85, 387-392, (1990) · Zbl 0702.62037 [8] Fan, Y.; Li, Q., Consistent model specification tests: omitted variables and semiparametric functional forms, Econometrica, 64, 865-890, (1996) · Zbl 0854.62038 [9] Gozalo, P.L., A consistent model specification test for nonparametric estimation of regression function models, Econometric theory, 9, 451-477, (1993) [10] Hall, P.; Horowitz, J.L., Bootstrap critical values for tests based on generalized-method-of-moments estimators, Econometrica, 64, 891-916, (1996) · Zbl 0854.62045 [11] Hansen, L.P.; Singleton, K., Generalized instrumental variable estimation of nonlinear rational expectations models, Econometrica, 50, 1269-1286, (1982) · Zbl 0497.62098 [12] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Annals of statistics, 21, 1926-1947, (1993) · Zbl 0795.62036 [13] Hong, Y.; White, H., Consistent specification testing via nonparametric series regressions, Econometrica, 63, 1133-1160, (1996) [14] Lewbel, A., Consistent nonparametric hypothesis tests with an application to slutsky symmetry, Journal of econometrics, 67, 379-401, (1995) · Zbl 0820.62042 [15] Li, Q.; Wang, S., A simple consistent booststrap test for a parametric regression function, Journal of econometrics, 87, 145-165, (1998) · Zbl 0943.62031 [16] Newey, W.K., Efficient instrumental variables estimation of nonlinear models, Econometrica, 58, 809-837, (1990) · Zbl 0728.62107 [17] Pollard, D., Convergence of stochastic processes, (1984), Springer Verlag New York · Zbl 0544.60045 [18] Pollard, D., Empirical processes: theory and applications, () · Zbl 0741.60001 [19] Whang, Y.-J., (), Unpublished manuscript [20] Whang, Y.-J., Consistent bootstrap tests of parametric regression functions, Journal of econometrics, 98, 27-46, (2000) · Zbl 0966.62018 [21] Wooldridge, J.M., A test for functional form against nonparametric alternatives, Econometric theory, 8, 452-475, (1992) [22] Yatchew, A.J., Nonparametric regression tests based on least squares, Econometric theory, 8, 435-451, (1992) [23] Zheng, J.X., A consistent test of functional form via nonparametric estimation techniques, Journal of econometrics, 75, 263-289, (1996) · Zbl 0865.62030
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