In this paper, we propose a general method for testing inequality
restrictions on nonparametric functions. Our framework includes many
nonparametric testing problems in a unified framework, with a number of
possible applications in auction models, game theoretic models, wage
inequality, and revealed preferences. Our test involves a one-sided version of
Lp functionals of kernel-type estimators (1≤p<∞) and is easy
to implement in general, mainly due to its recourse to the bootstrap method.
The bootstrap procedure is based on nonparametric bootstrap applied to
kernel-based test statistics, with estimated "contact sets." We provide
regularity conditions under which the bootstrap test is asymptotically valid
uniformly over a large class of distributions, including the cases that the
limiting distribution of the test statistic is degenerate. Our bootstrap test
is shown to exhibit good power properties in Monte Carlo experiments, and we
provide a general form of the local power function. As an illustration, we
consider testing implications from auction theory, provide primitive conditions
for our test, and demonstrate its usefulness by applying our test to real data.
We supplement this example with the second empirical illustration in the
context of wage inequality.Comment: 128 page