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 Abstract: 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.