TY - JOUR
T1 - Optimal testing for additivity in multiple nonparametric regression
AU - Abramovich, Felix
AU - De Feis, Italia
AU - Sapatinas, Theofanis
N1 - Funding Information:
Acknowledgment This work was supported by a bilateral agreement between the Department of Mathematics and Statistics of the University of Cyprus and the School of Mathematical Sciences of Tel Aviv University. Felix Abramovich would like to thank Theofanis Sapatinas for warm hospitality while visiting Nicosia to carry out part of this work. Finally, we would like to thank an anonymous referee for suggestions on improvements to this paper.
PY - 2009/9
Y1 - 2009/9
N2 - We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2([0, 1] d )-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.
AB - We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2([0, 1] d )-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.
KW - Additive models
KW - Functional hypothesis testing
KW - Minimax testing
KW - Nonparametric regression
KW - Wavelets
UR - https://www.scopus.com/pages/publications/68649128801
U2 - 10.1007/s10463-007-0164-y
DO - 10.1007/s10463-007-0164-y
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AN - SCOPUS:68649128801
SN - 0020-3157
VL - 61
SP - 691
EP - 714
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 3
ER -