| Type: | Package |
| Title: | Maximum Tangent Likelihood Estimation for Robust Linear Regression and Variable Selection |
| Version: | 1.2.1 |
| Encoding: | UTF-8 |
| Date: | 2025-04-30 |
| Maintainer: | Shaobo Li <shaobo.li@ku.edu> |
| Description: | Several robust estimators for linear regression and variable selection are provided. Included are Maximum tangent likelihood estimator by Qin, et al., (2017), arXiv preprint <doi:10.48550/arXiv.1708.05439>, least absolute deviance estimator and Huber regression. The penalized version of each of these estimator incorporates L1 penalty function, i.e., LASSO and Adaptive Lasso. They are able to produce consistent estimates for both fixed and high-dimensional settings. |
| URL: | https://github.com/shaobo-li/MTE |
| Depends: | R (≥ 3.1.0) |
| License: | GPL-3 |
| RoxygenNote: | 7.2.3 |
| Imports: | stats, quantreg, glmnet, rqPen |
| NeedsCompilation: | no |
| Packaged: | 2025-04-30 21:54:54 UTC; s674l142 |
| Author: | Shaobo Li [aut, cre], Yichen Qin [aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-05-01 13:30:13 UTC |
Least Absolute Deviance Estimator for Linear Regression
Description
Least Absolute Deviance Estimator for Linear Regression
Usage
LAD(X, y, intercept = FALSE)
Arguments
X |
design matrix |
y |
reponse vector |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
Value
coefficient estimates
Examples
set.seed(1989)
n=200; d=4
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(1, -1, 2, -2)
y=-2+X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
beta.ls=lm(y~X)$coeff
beta.LAD=LAD(X,y,intercept=TRUE)
cbind(c(-2,beta), beta.ls, beta.LAD)
LAD-Lasso for Linear Regression
Description
LAD-Lasso for Linear Regression
Usage
LADlasso(
X,
y,
beta.ini,
lambda = NULL,
adaptive = TRUE,
intercept = FALSE,
penalty.factor = rep(1, ncol(X))
)
Arguments
X |
design matrix, standardization is recommended. |
y |
reponse vector |
beta.ini |
initial estimates of beta. Using unpenalized LAD is recommended under high-dimensional setting. |
lambda |
regularization parameter of Lasso or adaptive Lasso (if adaptive=TRUE). |
adaptive |
logical input that indicates if adaptive Lasso is used. Default is TRUE. |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
penalty.factor |
can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet. |
Value
beta |
the regression coefficient estimates. |
fitted |
predicted response. |
iter.steps |
iteration steps. |
Examples
set.seed(2017)
n=200; d=50
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, 44))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.LADLasso=LADlasso(X, y, beta.ini=LAD(X, y))
beta.est=output.LADLasso$beta
Maximum Tangent-likelihood Estimation
Description
It estimates linear regression coefficient using MTE. The function produces robust estimates of linear regression. Outliers and contamination would be downweighted. It is robust to Gaussian assumption of the error term. Initial estimates need to be provided.
Usage
MTE(y, X, beta.ini, t, p, intercept = FALSE)
Arguments
y |
the response vector |
X |
design matrix |
beta.ini |
initial value of estimates, could be from OLS. |
t |
the tangent point. You may specify a sequence of values, so that the function automatically select the optimal one. |
p |
Taylor expansion order, up to 3. |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
Value
Returns estimates from MTE method.
beta |
the regression coefficient estimates |
fitted.value |
predicted response |
t |
the optimal tangent point through data-driven method |
Examples
set.seed(2017)
n=200; d=4
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(1, -1, 2, -2)
y=-2+X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
beta0=beta.ls=lm(y~X)$coeff
beta.MTE=MTE(y,X,beta0,0.1,2, intercept=TRUE)$beta
cbind(c(-2,beta), beta.ls, beta.MTE)
MTE-Lasso estimator
Description
MTELasso is the penalized MTE for robust estimation and variable selection for linear regression. It can deal with both fixed and high-dimensional settings.
Usage
MTElasso(
X,
y,
beta.ini,
p = 2,
lambda = NULL,
adaptive = TRUE,
t = 0.01,
intercept = TRUE,
penalty.factor = rep(1, ncol(X)),
...
)
Arguments
X |
design matrix, standardization is recommended. |
y |
response vector. |
beta.ini |
initial estimates of beta. If not specified, LADLasso estimates from |
p |
Taylor expansion order. |
lambda |
regularization parameter for LASSO, but not necessary if "adaptive=TRUE". |
adaptive |
logic argument to indicate if Adaptive-Lasso is used. Default is TRUE. |
t |
the tuning parameter that controls for the tradeoff between robustness and efficiency. Default is t=0.01. |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
penalty.factor |
can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet. |
... |
other arguments that are used in |
Value
It returns a sparse vector of estimates of linear regression. It has two types of penalty, LASSO and AdaLasso. Coordinate descent algorithm is used for iteratively updating coefficients.
beta |
sparse regression coefficient |
fitted |
predicted response |
Examples
set.seed(2017)
n=200; d=500
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, d-6))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.MTELasso=MTElasso(X, y, p=2, t=0.01)
beta.est=output.MTELasso$beta
Huber-Lasso estimator
Description
This function is L1 penalized Huber estimator for linear regression under both fixed and high-dimensional settings. Currently, the function does not support automatic selection of huber tuning parameter.
Usage
huber.lasso(
X,
y,
beta.ini,
lambda,
alpha = 2,
adaptive = TRUE,
intercept = TRUE,
penalty.factor = rep(1, ncol(X))
)
Arguments
X |
design matrix, standardization is recommended. |
y |
response vector. |
beta.ini |
initial estimates of beta. If not specified, LADLasso estimates from |
lambda |
regularization parameter of Lasso or adaptive Lasso (if adaptive=TRUE). |
alpha |
1/alpha is the huber tuning parameter. Larger alpha results in smaller portion of squared loss. |
adaptive |
logical input that indicates if adaptive Lasso is used. Default is TRUE. |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
penalty.factor |
can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet. |
Value
beta |
the regression coefficient estimates. |
fitted |
predicted response. |
iter.steps |
iteration steps. |
Examples
set.seed(2017)
n=200; d=500
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, d-6))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.HuberLasso=huber.lasso(X,y)
beta.est=output.HuberLasso$beta
Huber estimation for linear regression
Description
This function produces Huber estimates for linear regression. Initial estimates is required. Currently, the function does not support automatic selection of huber tuning parameter.
Usage
huber.reg(y, X, beta.ini, alpha, intercept = FALSE)
Arguments
y |
the response vector |
X |
design matrix |
beta.ini |
initial value of estimates, could be from OLS. |
alpha |
1/alpha is the huber tuning parameter delta. Larger alpha results in smaller portion of squared loss. |
intercept |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |
Value
beta |
the regression coefficient estimates |
fitted.value |
predicted response |
iter.steps |
iteration steps. |
Examples
set.seed(2017)
n=200; d=4
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(1, -1, 2, -2)
y=-2+X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
beta0=beta.ls=lm(y~X)$coeff
beta.huber=huber.reg(y, X, beta0, 2, intercept=TRUE)$beta
cbind(c(-2,beta), beta.ls, beta.huber)
Huber Loss
Description
Huber Loss
Usage
huberloss(r, alpha)
Arguments
r |
residual, y-Xbeta |
alpha |
1/alpha is the huber tuning parameter delta. Larger alpha results in smaller portion of squared loss. |
Value
it returns huber loss that will be called in Huber estimation.