# lambdaqut: Quantile Universal Threshold, regularization parameter for... In qut: Quantile Universal Threshold

## Description

Computes the Quantile Universal Threshold for GLM-lasso.

## Usage

 1 2 3 lambdaqut(y, X, family = gaussian, alpha.level = 0.05, M = 1000, qut.standardize = TRUE, intercept = TRUE, no.penalty = NULL, offset = NULL, bootstrap=TRUE,beta0=NA,method='lasso',fixbeta0=FALSE) 

## Arguments

 y response variable. Quantitative for family=gaussian, or family=poisson (non-negative counts). For family=binomial should be a factor with two levels. X input matrix, of dimension n x p; each row is an observation vector. family response type (see above). Default is gaussian. alpha.level level, such that quantile τ=(1-alpha.level)/γ. Default is 0.05. M number of Monte Carlo Simulations to estimate the distribution Λ. Default is 1000. qut.standardize standardize matrix X with a quantile-based standardization. Default is TRUE. intercept should intercept(s) be fitted (default=TRUE) or set to zero (FALSE). no.penalty unpenalized subset of covariates. offset a vector of length n that is included in the linear predictor. Useful for the "poisson" family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is NULL. bootstrap set TRUE if it is desired to bootstrap matrix X when computing the Quantile Universal Threshold (Random scenario). Default is TRUE. beta0 coefficients of the unpenalized covariates for generating the null data for the Quantile Universal Threshold. By default is NA and it is estimated using the unpenalized covariates and/or the intercept if TRUE. If it is desired to set beta0 in advance, then it should be a vector of size the number of unpenalized covariates including the intercept if intercept=TRUE, in the same order. If there are not unpenalized covariates and intercept=TRUE, then it must be a real number. method objective function for the zero thresholding. Select lasso for GLM-lasso or sqrtlasso for Square-root lasso. fixbeta0 used when beta0 is numeric. When TRUE, it does not estimate beta0 for each monte carlo simulation.

## Value

 lambda value of the Quantile Universal Threshold. Xnew standardized matrix X; Xnew=X\timesscale.factor. scale.factor scale factor for Xnew. lambda.max smallest lambda that sets the lasso estimates to the zero vector. beta0  estimated value of the intercept when family is not gaussian.

Jairo Diaz

## References

C. Giacobino, J. Diaz, S. Sardy, N. Hengartner. Quantile universal threshold for model selection. 2016 Jianqing Fan, Shaojun Guo and Ning Hao. Variance estimation using refitted cross-validation in ultrahigh dimensional regression. Journal of the Royal Statistical Society: Series B. 2012 Stephen Reid, Robert Tibshirani, and Jerome Friedman. A Study of Error Variance Estimation in Lasso Regression. 2013

qut
 1 2 3 4  X=matrix(rnorm(20*200),20,200) y=rnorm(20)+1 lambda=lambdaqut(y,X,family=gaussian)