Test and Measure for Partial Mean Dependence Based on Machine Learning Methods
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909216779796480 |
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| author | Cai, Leheng Guo, Xu Zhong, Wei |
| author_facet | Cai, Leheng Guo, Xu Zhong, Wei |
| contents | It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based on machine learning methods and data splitting. The test statistic converges to the standard chi-squared distribution under the null hypothesis while it converges to a normal distribution under the fixed alternative hypothesis. Power enhancement and algorithm stability are also discussed. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of $Y$ given $W$ after controlling for the nonlinear effect of $Z$. We present the appealing theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-$N$ convergence rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there are no conditional covariates $Z$, we introduce a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are also conducted to compare with existing approaches and to demonstrate the validity and flexibility of our proposed procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12874 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Test and Measure for Partial Mean Dependence Based on Machine Learning Methods Cai, Leheng Guo, Xu Zhong, Wei Methodology It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based on machine learning methods and data splitting. The test statistic converges to the standard chi-squared distribution under the null hypothesis while it converges to a normal distribution under the fixed alternative hypothesis. Power enhancement and algorithm stability are also discussed. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of $Y$ given $W$ after controlling for the nonlinear effect of $Z$. We present the appealing theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-$N$ convergence rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there are no conditional covariates $Z$, we introduce a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are also conducted to compare with existing approaches and to demonstrate the validity and flexibility of our proposed procedures. |
| title | Test and Measure for Partial Mean Dependence Based on Machine Learning Methods |
| topic | Methodology |
| url | https://arxiv.org/abs/2212.12874 |