1d:T7fb,# L2E convex regression `L2E_convex` performs convex regression under the L2 criterion. Available methods include proximal gradient descent (PG) and majorization-minimization (MM). ```r L2E_convex( y, beta, tau, method = "MM", max_iter = 100, tol = 1e-04, Show.Time = TRUE ) ``` ## Arguments - `y`: Response vector - `beta`: Initial vector of regression coefficients - `tau`: Initial precision estimate - `method`: Available methods include PG and MM. MM by default. - `max_iter`: Maximum number of iterations - `tol`: Relative tolerance - `Show.Time`: Report the computing time ## Returns Returns a list object containing the estimates for beta (vector) and tau (scalar), the number of outer block descent iterations until convergence (scalar), and the number of inner iterations per outer iteration for updating beta (vector) and tau or eta (vector) ## Examples ```r set.seed(12345) n <- 200 tau <- 1 x <- seq(-2, 2, length.out=n) f <- x^4 + x y <- f + (1/tau) * rnorm(n) ## Clean Data plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray') lines(x, f, lwd=3) tau <- 1 b <- y ## Least Squares method cvx <- fitted(cobs::conreg(y, convex=TRUE)) ## MM method sol_mm <- L2E_convex(y, b, tau) ## PG method sol_pg <- L2E_convex(y, b, tau, method='PG') plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray') lines(x, f, lwd=3) lines(x, cvx, col='blue', lwd=3) ## LS lines(x, sol_mm$beta, col='red', lwd=3) ## MM lines(x, sol_pg$beta, col='dark green', lwd=3) ## PG ## Contaminated Data ix <- 0:9 y[45 + ix] <- 14 + rnorm(10) plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray') lines(x, f, lwd=3) tau <- 1 b <- y cvx <- fitted(cobs::conreg(y, convex=TRUE)) sol_mm <- L2E_convex(y, b, tau) sol_pg <- L2E_convex(y, b, tau, method='PG') plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray') lines(x, f, lwd=3) lines(x, cvx, col='blue', lwd=3) ## LS lines(x, sol_mm$beta, col='red', lwd=3) ## MM lines(x, sol_pg$beta, col='dark green', lwd=3) ## PG

L2E_convex function