TY - JOUR
T1 - Adaptive-to-Model Hybrid of Tests for Regressions
AU - Li, Lingzhu
AU - Zhu, Xuehu
AU - Zhu, Lixing
N1 - Funding information:
The authors gratefully acknowledge two grants from the University Grants Council of Hong Kong (HKBU123017/17 and HKBU123028/18), an NSFC (grant no. NSFC11671042) and a grant from China Postdoctoral Science Foundation (grant no. 2020M683456). The first two authors are the co-first authors. The thanks go to Editor, Associate editor and two referees for their constructive suggestions that led to a significant improvement of an early article. The authors are also graceful to Drs. Escanciano, Pardo-Fernández, and Van Keilegom for the useful discussions.
Publisher Copyright:
© 2021 American Statistical Association
PY - 2023/3
Y1 - 2023/3
N2 - In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. In contrast, empirical process-based tests can, at the fastest possible rate, detect local alternatives distinct from the null model, yet are less sensitive to oscillating alternatives and rely on Monte Carlo approximation for critical value determination, which is costly in computation. We propose an adaptive-to-model hybrid of moment and conditional moment-based tests to fully inherit the merits of these two types of tests and avoid the shortcomings. Further, such a hybrid makes nonparametric estimation-based tests, under the alternatives, also share the merits of existing empirical process-based tests. The methodology can be readily applied to other kinds of data and construction of other hybrids. As a by-product in sufficient dimension reduction field, a study on residual-related central mean subspace and central subspace for model adaptation is devoted to showing when alternative models can be indicated and when cannot. Numerical studies are conducted to verify the powerfulness of the proposed test.
AB - In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. In contrast, empirical process-based tests can, at the fastest possible rate, detect local alternatives distinct from the null model, yet are less sensitive to oscillating alternatives and rely on Monte Carlo approximation for critical value determination, which is costly in computation. We propose an adaptive-to-model hybrid of moment and conditional moment-based tests to fully inherit the merits of these two types of tests and avoid the shortcomings. Further, such a hybrid makes nonparametric estimation-based tests, under the alternatives, also share the merits of existing empirical process-based tests. The methodology can be readily applied to other kinds of data and construction of other hybrids. As a by-product in sufficient dimension reduction field, a study on residual-related central mean subspace and central subspace for model adaptation is devoted to showing when alternative models can be indicated and when cannot. Numerical studies are conducted to verify the powerfulness of the proposed test.
KW - Global smoothing test
KW - Local smoothing test
KW - Model adaptation
KW - Oscillating model
UR - http://www.scopus.com/inward/record.url?scp=85111447334&partnerID=8YFLogxK
U2 - 10.1080/01621459.2021.1941052
DO - 10.1080/01621459.2021.1941052
M3 - Journal article
AN - SCOPUS:85111447334
SN - 0162-1459
VL - 118
SP - 514
EP - 523
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 541
ER -