The Size Problem of Kernel Based Bootstrap Tests when

The Size Problem of Kernel Based Bootstrap Tests when the
Null is Nonparametric
Jorge Barrientos-Marín, Universidad de Antioquia
Stefan Sperlich, Georg-August Universität Göttingen
February 14th 2007, 12:00-13:00 hs
E.T.S. de Ingenieros de Minas, Laboratorio 11
In non- and semiparametric testing, the wild bootstrap is a standard
method for determining the critical values of tests. While there exists an
increasing literature on how to find a proper smoothing parameter for the
nonparametric alternative, almost nothing is known on how to choose a smoothing
parameter in practice for the null hypothesis if it is also semi- or
nonparametric. We do know that at least asymptotically oversmoothing is necessary
in the pre-estimation of the null model for generating the bootstrap samples, see
H\"{a}rdle and Marron (1990,1991). However, in practice this knowledge is of
little help. The same can be said about various parameters and procedures to be
chosen in practice when performing such tests. In this article we discuss all
these choice questions. In particular we study the problem of bandwidth choice
for the pre-estimation to generate bootstrap samples. As an alternative, we also
discuss briefly the possibility of subsampling.