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

Xuehu Zhu, Xu Guo, Lixing Zhu

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1193-1204
Number of pages12
JournalStatistics and Computing
Volume27
Issue number5
DOIs
StatePublished - Sep 1 2017

Fingerprint

Single-index Model
Parametric Model
Dimension Reduction
Null
Sampling Distribution
Null Distribution
Covariates
Alternatives
Marked Empirical Process
Sampling
Model
Bootstrap Method
Ridge
Approximation
Model structures
Null hypothesis
Approximation Methods
Dimensionality
Linear Combination
Regression Model

All Science Journal Classification (ASJC) codes

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

Cite this

Zhu, Xuehu ; Guo, Xu ; Zhu, Lixing. / An adaptive-to-model test for partially parametric single-index models. In: Statistics and Computing. 2017 ; Vol. 27, No. 5. pp. 1193-1204.
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An adaptive-to-model test for partially parametric single-index models. / Zhu, Xuehu; Guo, Xu; Zhu, Lixing.

In: Statistics and Computing, Vol. 27, No. 5, 01.09.2017, p. 1193-1204.

Research output: Contribution to journalArticle

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