# Partial Ridge Computes the Partial Ridge estimator. ```r 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). ## Returns 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 ```r 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) # 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)) ```

PartRidge function