lassofit {FAS}

Fits effective noise of LASSO regressions

Description

Fits effective noise of LASSO regressions.

Usage

lassofit(x, y, q.levels = c(0.90, 0.95, 0.99), p.value = FALSE,
         numboot = 1000L, nlambda = 100L,
         lambda.factor = ifelse(nobs < nvars, 1e-02, 1e-04), 
         lambda = NULL, pf = rep(1, nvars),
         dfmax = nvars + 1, 
         pmax = min(dfmax * 1.2, nvars), standardize = FALSE, 
         intercept = FALSE, eps = 1e-08, maxit = 1000000L)

Arguments

x

T by p data matrix, where T and p respectively denote the sample size and the number of regressors.

y

T by 1 response variable.

q.levels

quantile levels of effective noise.

p.value

whether pvalue should be computed. Default is FALSE.

numboot

bootstrap replications.

nlambda

number of \lambda's to use in the regularization path; used if lambda = NULL.

lambda.factor

The factor for getting the minimal \lambda in the \lambda sequence, where min(lambda) = lambda.factor * max(lambda). max(lambda) is the smallest value of lambda for which all coefficients are zero. λ _max is determined for each \gamma tuning parameter separately. The default depends on the relationship between T (the sample size) and p (the number of predictors). If T < p, the default is 0.01. If T > p, the default is 0.0001, closer to zero. The smaller the value of lambda.factor is, the denser is the fit for λ_min. Used only if lambda = NULL.

lambda

a user-supplied lambda sequence. By leaving this option unspecified (recommended), users can have the program compute its own lambda sequence based on nlambda and lambda.factor. It is better to supply, if necessary, a decreasing sequence of lambda values than a single (small) value, as warm-starts are used in the optimization algorithm. The program will ensure that the user-supplied \lambda sequence is sorted in decreasing order before fitting the model.

pf

the ℓ₁ penalty factor of length p used for the adaptive sg-LASSO. Separate ℓ₁ penalty weights can be applied to each coefficient to allow different ℓ₁ + ℓ_2,1 shrinkage. Can be 0 for some variables, which imposes no shrinkage, and results in that variable always be included in the model. Default is 1 for all variables.

dfmax

the maximum number of variables allowed in the model. Useful for very large p when a partial path is desired. Default is p+1. In case method='fe', dfmax is ignored.

pmax

the maximum number of coefficients allowed ever to be nonzero. For example, once β_i ≠ 0 for some i ∈ [p], no matter how many times it exits or re-enters the model through the path, it will be counted only once. Default is min(dfmax*1.2, p).

standardize

logical flag for variable standardization, prior to fitting the model sequence. The coefficients are always returned to the original scale. It is recommended to keep standardize=TRUE. Default is FALSE.

intercept

whether intercept be fitted (TRUE) or set to zero (FALSE). Default is FALSE. In case method='pooled', intercept=TRUE is forced. In case method='fe', intercept=FALSE is forced and entity specific intercepts are fitted in a separate output variable a0.

eps

convergence threshold for block coordinate descent. Each inner block coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance. Defaults value is 1e-8.

maxit

maximum number of outer-loop iterations allowed at fixed lambda values. Default is 1e6. If the algorithm does not converge, consider increasing maxit.

Details

Fits effective noise of LASSO regressions.

Value

lassofit object.

Author(s)

Jonas Striaukas

Examples

set.seed(1)
x = matrix(rnorm(100 * 20), 100, 20)
beta = c(5,4,3,2,1,rep(0, times = 15))
y = x%*%beta + rnorm(100)
lassofit(x = x, y = y)