Testing functional inequalities
Copyright policy )Testing functional inequalities
This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of $L_p$-type functionals of kernel estimators $(1 \leq p < \infty)$. Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives. Furthermore, we establish conditions under which the tests have nontrivial local power against Pitman local alternatives. Some results from Monte Carlo simulations are presented.
60 pages, 4 figures
- Department of Economics Indonesia
- University of British Columbia Canada
- SEOUL NATIONAL UNIVERSITY
- Institute for Fiscal Studies United Kingdom
- Department of Economics Switzerland
FOS: Computer and information sciences, conditional moment inequalities, Poissonization, 62G10, 62G08, 62G20, Mathematics - Statistics Theory, local power, Statistics Theory (math.ST), Lp norm, Methodology (stat.ME), Asymptotic properties of nonparametric inference, kernel estimation, FOS: Mathematics, C14, Nonparametric regression and quantile regression, Nonparametric hypothesis testing, Applications of statistics to economics, Statistics - Methodology, C12, \(L_p\) norm, ddc:330, Density estimation, Kernel estimation, one-sided test
FOS: Computer and information sciences, conditional moment inequalities, Poissonization, 62G10, 62G08, 62G20, Mathematics - Statistics Theory, local power, Statistics Theory (math.ST), Lp norm, Methodology (stat.ME), Asymptotic properties of nonparametric inference, kernel estimation, FOS: Mathematics, C14, Nonparametric regression and quantile regression, Nonparametric hypothesis testing, Applications of statistics to economics, Statistics - Methodology, C12, \(L_p\) norm, ddc:330, Density estimation, Kernel estimation, one-sided test
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