PartRidge: Partial Ridge

In xinxuyale/HDCI: High Dimensional Confidence Interval Based on Lasso and Bootstrap

Description

Computes the Partial Ridge estimator.

Usage

PartRidge(x, y, lambda2 = 0, varset, 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.
lambda2	Tuning parameter for the Partial Ridge. The default value is 0, which gives back to the OLS estimator.
varset	A set indicating which variable/predictors are not penalized. Partial Ridge puts l2 penalty only on the coefficients of the variables/predictors not included in the varset.
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).

Details

This function computes the Partial Ridge estimator, which adds l2 penalty only on the coefficients of variabels/predictors not included in the set varset, to the loss function (residual sum of squares).

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.
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.
lambda2	The value of lambda2.

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)

## Partial Ridge Regression
# Lasso
set.seed(0)
obj.escv <- escv.glmnet(x, y)
obj <- Lasso(x, y, lambda = obj.escv$lambda.cv)
# variable set
betalasso <- obj$beta
selectvar <- betalasso != 0
# partial ridge 
PR.obj <- PartRidge(x = x, y = y, lambda2 = 1/n, varset = selectvar)
# parial ridge estimate of the regression coefficients
beta <- PR.obj$beta
# intercept term
beta0 <- PR.obj$beta0
# prediction
mypredict(PR.obj, newx = matrix(rnorm(10*p), 10, p))

xinxuyale/HDCI documentation built on May 23, 2019, 9:51 a.m.