### Abstract

Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a partial dimension reduction adaptive-to-model testing procedure that can be omnibus against general global alternative models although it fully use the dimension reduction structure under the null hypothesis. This feature is because that the procedure can automatically adapt to the null and alternative models, and thus greatly overcomes the dimensionality problem. Second, to achieve the above goal, we propose a ridge-type eigenvalue ratio estimate to automatically determine the number of linear combinations of the covariates under the null and alternative hypotheses. Third, a Monte-Carlo approximation to the sampling null distribution is suggested. Unlike existing bootstrap approximation methods, this gives an approximation as close to the sampling null distribution as possible by fully utilising the dimension reduction model structure under the null model. Simulation studies and real data analysis are then conducted to illustrate the performance of the new test and compare it with existing tests.

Original language | English (US) |
---|---|

Pages (from-to) | 1193-1204 |

Number of pages | 12 |

Journal | Statistics and Computing |

Volume | 27 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics

### Cite this

*Statistics and Computing*,

*27*(5), 1193-1204. https://doi.org/10.1007/s11222-016-9680-z

}

*Statistics and Computing*, vol. 27, no. 5, pp. 1193-1204. https://doi.org/10.1007/s11222-016-9680-z

**An adaptive-to-model test for partially parametric single-index models.** / Zhu, Xuehu; Guo, Xu; Zhu, Lixing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An adaptive-to-model test for partially parametric single-index models

AU - Zhu, Xuehu

AU - Guo, Xu

AU - Zhu, Lixing

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a partial dimension reduction adaptive-to-model testing procedure that can be omnibus against general global alternative models although it fully use the dimension reduction structure under the null hypothesis. This feature is because that the procedure can automatically adapt to the null and alternative models, and thus greatly overcomes the dimensionality problem. Second, to achieve the above goal, we propose a ridge-type eigenvalue ratio estimate to automatically determine the number of linear combinations of the covariates under the null and alternative hypotheses. Third, a Monte-Carlo approximation to the sampling null distribution is suggested. Unlike existing bootstrap approximation methods, this gives an approximation as close to the sampling null distribution as possible by fully utilising the dimension reduction model structure under the null model. Simulation studies and real data analysis are then conducted to illustrate the performance of the new test and compare it with existing tests.

AB - Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a partial dimension reduction adaptive-to-model testing procedure that can be omnibus against general global alternative models although it fully use the dimension reduction structure under the null hypothesis. This feature is because that the procedure can automatically adapt to the null and alternative models, and thus greatly overcomes the dimensionality problem. Second, to achieve the above goal, we propose a ridge-type eigenvalue ratio estimate to automatically determine the number of linear combinations of the covariates under the null and alternative hypotheses. Third, a Monte-Carlo approximation to the sampling null distribution is suggested. Unlike existing bootstrap approximation methods, this gives an approximation as close to the sampling null distribution as possible by fully utilising the dimension reduction model structure under the null model. Simulation studies and real data analysis are then conducted to illustrate the performance of the new test and compare it with existing tests.

UR - http://www.scopus.com/inward/record.url?scp=84976498734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976498734&partnerID=8YFLogxK

U2 - 10.1007/s11222-016-9680-z

DO - 10.1007/s11222-016-9680-z

M3 - Article

AN - SCOPUS:84976498734

VL - 27

SP - 1193

EP - 1204

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 5

ER -