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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.27813 |
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| _version_ | 1866909004405407744 |
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| author | Hill, Jonathan B. |
| author_facet | Hill, Jonathan B. |
| contents | We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be screened may be large $p$ $>>$ $n$, and growing at an exponential rate, provided $\ln (p)$ $=$ $o(n^{a})$ for some $a$ $>$ $0$ that depends on memory decay and the growth of higher moments. We study the problem of correlation screening in a high dimensional marginal regression setting, assuming so-called \textit{physical dependence} in a time series setting. We entirely sidestep covariance matrix estimation and adaptive re-sampling by working with a max-statistic over the many computed parameters. Thus we do not need endogenous selection of the most relevant predictor index yielding non-uniform asymptotics, nor do we need a post-estimation Bonferroni correction. The non-standard limit distribution arising from the maximum of an increasing number of estimators is easily approximated by a multiplier (wild) block bootstrap. The max-test controls for size well, performs well against various deviations from the null, including very slight deviations with a weak or sparse signal. A numerical experiment is performed and an empirical example with the VIX volatility index is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27813 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A High Dimensional Wild Bootstrap Max-Test for Detecting the Presence of Significant Predictors Hill, Jonathan B. Statistics Theory 62F07, 62H15, 62G10 We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be screened may be large $p$ $>>$ $n$, and growing at an exponential rate, provided $\ln (p)$ $=$ $o(n^{a})$ for some $a$ $>$ $0$ that depends on memory decay and the growth of higher moments. We study the problem of correlation screening in a high dimensional marginal regression setting, assuming so-called \textit{physical dependence} in a time series setting. We entirely sidestep covariance matrix estimation and adaptive re-sampling by working with a max-statistic over the many computed parameters. Thus we do not need endogenous selection of the most relevant predictor index yielding non-uniform asymptotics, nor do we need a post-estimation Bonferroni correction. The non-standard limit distribution arising from the maximum of an increasing number of estimators is easily approximated by a multiplier (wild) block bootstrap. The max-test controls for size well, performs well against various deviations from the null, including very slight deviations with a weak or sparse signal. A numerical experiment is performed and an empirical example with the VIX volatility index is provided. |
| title | A High Dimensional Wild Bootstrap Max-Test for Detecting the Presence of Significant Predictors |
| topic | Statistics Theory 62F07, 62H15, 62G10 |
| url | https://arxiv.org/abs/2604.27813 |