## High-dimensional simultaneous inference with the bootstrap.(English)Zbl 06833591

Summary: We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous inference for parameters in groups $$G$$, where $$p \gg n$$, $$s_0 = o(n^{1/2}/\{\log (p) \log (|G|)^{1/2}\})$$ and $$\log (|G|) = o(n^{1/7})$$, with $$p$$ the number of variables, $$n$$ the sample size and $$s_0$$ the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi [L. Meier et al., hdi: high-dimensional inference. R package version 0.1-6 (2016)].

### MSC:

 62J07 Ridge regression; shrinkage estimators (Lasso) 62F40 Bootstrap, jackknife and other resampling methods

### Software:

selectiveInference; R; hdm; hdi
Full Text:

### References:

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