Modified Least Squares
Computes modified Least Squares estimate.
mls(x, y, tau = 0, standardize = TRUE, intercept = TRUE)
x |
Input matrix as in glmnet, of dimension nobs x nvars; each row is an observation vector. |
y |
Response variable. |
tau |
Tuning parameter in modified Least Squares (mls). Default value is 0, which corresponds to Ordinary Least Squares (OLS). |
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). |
The function is used to compute the modified Least Squares (mLS) estimator defined in the paper: Liu H, Yu B. Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression. Electronic Journal of Statistics, 2013, 7.
A list consisting of the following elements is returned.
beta |
The mLS coefficient 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. |
tau |
The tuning parameter in mLS. |
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)
## modified Least Squares
set.seed(0)
obj <- mls(x = x[, 1:20], y = y)
# the OLS estimate of the regression coefficients
obj$beta
# intercept term
obj$beta0
# prediction
mypredict(obj, newx = matrix(rnorm(10*20), 10, 20))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.