TY  - GEN
Y1  - 1998/10/26/
N1  - auch veröffentlicht in: Journal of Time Series Analysis
Volume 23, Issue 5, pages 555?585, September 2002
TI  - Properties of the Nonparametric Autoregressive Bootstrap
CY  - Heidelberg
AV  - public
KW  - Bootstrap
KW  -  nonparametric autoregression
KW  -  coupling
KW  -  geometric ergodicity
KW  -  consistence
ID  - heidok20796
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20796/
EP  - 26
A1  - Franke, Jürgen
A1  - Kreiss, Jens-Peter
A1  - Mammen, Enno
A1  - Neumann, Michael H.
N2  - We prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. To this end, we revisit this problem for nonparametric autoregressive processes and give some quantitative conditions (i.e., with explicit constants) under which the mixing coefficients of such processes can be bounded by some exponentially decaying sequence. This is achieved by using well-established coupling techniques.Then we apply the result to the bootstrap process and propose some particularestimators of the autoregression function and of the density of the innovations for which the bootstrap process has the desired properties.Moreover, by using some "decoupling" argument, we show that the stationary density of the bootstrap process converges to that of the original process. As an illustration, we use the proposed bootstrap method to construct simultaneous confidence bands and supremum-type tests for the autoregression function as well as to approximate the distribution of the least squares estimator in a certain parametric model.
ER  -