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LPR

Lasso Partial Ridge


Description

Computes the two-stage estimator Lasso+Partial Ridge.

Usage

LPR(x, y, lambda = NULL, fix.lambda = TRUE, lambda2, cv.method = "cv", nfolds = 10, 
    foldid, cv.OLS = TRUE, tau = 0, parallel = FALSE, standardize = TRUE, intercept = 
    TRUE, ...)

Arguments

x

Input matrix as in glmnet, of dimension nobs x nvars; each row is an observation vector.

y

Response variable.

lambda

lambda: A value of lambda - default is NULL. lambda should be given a value when fix.lambda=TRUE.

fix.lambda

If TRUE, computes Lasso+Partial Ridge estimator for a fix value of lambda given by the argument "lambda"; otherwise, computes Lasso+Partial Ridge estimator for the value of lambda choosing by cv/cv1se/escv.

lambda2

Tuning parameter in the Partial Ridge. If missing, lambda2 will be set to 1/nobs, where nobs is the number of observations.

cv.method

The method used to select lambda – can be cv, cv1se, and escv; the default is cv. cv.method is useful only when fix.lambda=FALSE.

nfolds, foldid, cv.OLS, tau, parallel

Arguments that can be passed to escv.glmnet (useful only when fix.lambda=FALSE). Note that, the default value of cv.OLS is TRUE, which means using Lasso+OLS in the cv fits.

standardize

Logical flag for x variable standardization, prior to fitting the model. Default is standardize=TRUE.

intercept

Should intercept be fitted (default is TRUE) or set to zero (FALSE).

...

Other arguments that can be passed to glmnet.

Details

This function computes the Lasso+Partial Ridge estimator for a give value of lambda (if fix.lambda=TRUE) or for the value of lambda choosing by cv/cv1se/escv (if fix.lambda=FALSE).

Value

A list consisting of the following elements is returned.

beta

The Lasso+Partial Ridge estimator for the coefficients of variables/predictors.

beta0

A value of intercept term.

lambda

The value/values of lambda.

lambda2

The value of lambda2.

meanx

The mean vector of variables/predictors if intercept=TRUE, otherwise is a vector of 0's.

mu

The mean of the response if intercept=TRUE, otherwise is 0.

normx

The vector of standard error of variables/predictors if standardize=TRUE, otherwise is a vector of 1's.

tau

Tuning parameter in modified Least Squares (mls).

Examples

library("glmnet")
library("mvtnorm") 

## generate the data
set.seed(2015)
n <- 200      # number of obs
p <- 500
s <- 10
beta <- rep(0, p)
beta[1:s] <- runif(s, 1/3, 1)
x <- rmvnorm(n = n, mean = rep(0, p), method = "svd")
signal <- sqrt(mean((x %*% beta)^2))
sigma <- as.numeric(signal / sqrt(10))  # SNR=10
y <- x %*% beta + rnorm(n)

## Lasso+Partial Ridge estimator
# for a given value of lambda
set.seed(0)
obj.escv <- escv.glmnet(x, y)
obj <- LPR(x, y, lambda = obj.escv$lambda.cv)
# Lasso+OLS estimate of the regression coefficients
obj$beta
# intercept term
obj$beta0
# prediction
mypredict(obj, newx = matrix(rnorm(10*p), 10, p))

# for lambda choosing by cross-validation (cv) which uses Lasso+OLS in the cv fit
set.seed(0)
obj <- LPR(x, y, fix.lambda = FALSE)

# for lambda choosing by cross-validation (cv) which uses Lasso in the cv fit
set.seed(0)
obj <- LPR(x, y, fix.lambda = FALSE, cv.OLS = FALSE)

HDCI

High Dimensional Confidence Interval Based on Lasso and Bootstrap

v1.0-2
GNU General Public License version 2
Authors
Hanzhong Liu, Xin Xu, Jingyi Jessica Li
Initial release
2017-06-06

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