High-dimensional simultaneous inference with the bootstrap

• Ruben Dezeure ^[1] ; Peter Bühlmann ^[1] ; Cun-Hui Zhang ^[1]
  1. [1] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 4, 2017, págs. 685-719
• Idioma: inglés
• DOI: 10.1007/s11749-017-0554-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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≫n, s0=o(n1/2/{log(p)log(|G|)1/2}) and log(|G|)=o(n1/7), with p the number of variables, n the sample size and s0 the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi (Meier et al. hdi: high-dimensional inference. R package version 0.1-6, 2016).