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(2017).\n\n\n```r\nStep(X, Y, M = 500, alpha = 0.05)\n```\n\n## Arguments\n\n- `X`: n times p design matrix.\n- `Y`: Response variable.\n- `M`: The number of bootstrap replications (default 500).\n- `alpha`: The nominal level alpha (default 0.05).\n\n## Returns\n\nA vector indicating which hypotheses are being rejected.\n\n\n\n## References\n\nZhang, X., and Cheng, G. (2017) Simultaneous Inference for High-dimensional Linear Models, **Journal of the American Statistical Association**, 112, 757-768.\n\n## Examples\n\n```r\n## The function is intended for large n and p.\n## Use small p here for illustration purpose only.\nn <- 100\np <- 10\ns0 <- 3\nset <- 1:s0\nSigma <- matrix(NA, p, p)\nfor (i in 1:p) Sigma[i,] <- 0.9^(abs(i-(1:p)))\nX <- matrix(rnorm(n*p), n, p)\nX <- t(t(chol(Sigma))%*%t(X))\nbeta <- rep(0,p)\nbeta[1:s0] <- runif(s0,1,2)\nY <- X%*%beta+rt(n,4)/sqrt(2)\nStep(X, Y, M=500, alpha=0.05)\n```"}]}]}]}]}]}],["$","div",null,{"className":"lg:w-1/3 lg:border-l px-1 sm:px-8 pt-8 sm:pt-1","children":[["$","div",null,{"className":"mb-8 space-y-8","children":[["$","a",null,{"href":"/packages/SILM","className":"w-full inline-flex items-center justify-center p-4 text-base font-medium text-gray-600 rounded-lg bg-muted hover:text-gray-900 hover:bg-gray-100 dark:text-gray-400 dark:bg-gray-800 dark:hover:bg-gray-700 dark:hover:text-white","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-package mr-4 h-6 w-6","children":[["$","path","1c824w",{"d":"m7.5 4.27 9 5.15"}],["$","path","hh9hay",{"d":"M21 8a2 2 0 0 0-1-1.73l-7-4a2 2 0 0 0-2 0l-7 4A2 2 0 0 0 3 8v8a2 2 0 0 0 1 1.73l7 4a2 2 0 0 0 2 0l7-4A2 2 0 0 0 21 16Z"}],["$","path","g66t2b",{"d":"m3.3 7 8.7 5 8.7-5"}],["$","path","d0xqtd",{"d":"M12 22V12"}],"$undefined"]}],["$","span",null,{"className":"w-full","children":["SILM"," package"]}]]}],["$","a",null,{"href":"https://cran.r-project.org/web/packages/SILM/SILM.pdf","target":"_blank","rel":"noopener noreferrer","className":"w-full inline-flex items-center justify-center p-4 text-base font-medium text-gray-600 rounded-lg bg-muted hover:text-gray-900 hover:bg-gray-100 dark:text-gray-400 dark:bg-gray-800 dark:hover:bg-gray-700 dark:hover:text-white","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-book mr-4 h-6 w-6","children":[["$","path","t4utmx",{"d":"M4 19.5v-15A2.5 2.5 0 0 1 6.5 2H20v20H6.5a2.5 2.5 0 0 1 0-5H20"}],"$undefined"]}],["$","span",null,{"className":"w-full","children":"Read PDF manual"}]]}]]}],["$","div",null,{"children":["$","ul",null,{"className":"space-y-4 my-12","children":[["$","li",null,{"children":["$","div",null,{"className":"inline-flex","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-user mr-4 h-6 w-6","children":[["$","path","975kel",{"d":"M19 21v-2a4 4 0 0 0-4-4H9a4 4 0 0 0-4 4v2"}],["$","circle","17ys0d",{"cx":"12","cy":"7","r":"4"}],"$undefined"]}]," Maintainer: ","Xianyang Zhang"]}]}],["$","li",null,{"children":["$","div",null,{"className":"inline-flex","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-scale mr-4 h-6 w-6","children":[["$","path","7g6ntu",{"d":"m16 16 3-8 3 8c-.87.65-1.92 1-3 1s-2.13-.35-3-1Z"}],["$","path","ijws7r",{"d":"m2 16 3-8 3 8c-.87.65-1.92 1-3 1s-2.13-.35-3-1Z"}],["$","path","1b0cd5",{"d":"M7 21h10"}],["$","path","108xh3",{"d":"M12 3v18"}],["$","path","3gwbw2",{"d":"M3 7h2c2 0 5-1 7-2 2 1 5 2 7 2h2"}],"$undefined"]}]," License: ","GPL-3"]}]}],["$","li",null,{"children":["$","div",null,{"className":"inline-flex","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-calendar-days mr-4 h-6 w-6","children":[["$","path","1cmpym",{"d":"M8 2v4"}],["$","path","4m81vk",{"d":"M16 2v4"}],["$","rect","1hopcy",{"width":"18","height":"18","x":"3","y":"4","rx":"2"}],["$","path","8toen8",{"d":"M3 10h18"}],["$","path","6423bh",{"d":"M8 14h.01"}],["$","path","1etili",{"d":"M12 14h.01"}],["$","path","1gbofw",{"d":"M16 14h.01"}],["$","path","lrp35t",{"d":"M8 18h.01"}],["$","path","mhygvu",{"d":"M12 18h.01"}],["$","path","kzsmim",{"d":"M16 18h.01"}],"$undefined"]}],"Last published: ","2019-01-09"]}]}],null]}]}],["$","div",null,{"className":"mb-8","children":[["$","p",null,{"className":"border-b pb-1","children":"Useful links"}],["$","ul",null,{"className":"space-y-2 my-4","children":[]}]]}],["$","$L1d",null,{"Package":"SILM"}]]}]]}]}]]