# [Robust estimator for regression models This function is for Robust regression by the IRLS algorithm. It integrates child functions contained in Tirls.r and Hirls.r. ```r robReg( x1, y1, wf = "T", scale = "AAD", rt = rep(1, length(y1)), tp = 8, rp.max = 150, cg.rt = 0.01 ) ``` ## Arguments - `x1`: explanatory variable in regression (a vector or a matrix) - `y1`: objective variable in regression (a vector) - `wf`: weight function ("T" for Tukey's biweight, and "H" for Huber weight) - `scale`: scale for residuals. "AAD"(default) or "MAD". - `rt`: sample weight (default 1) - `tp`: tuning parameter (tp=4, 6 or 8) for weight function. Smaller figure is more robust. - `rp.max`: The maximum number of iteration (default 150) - `cg.rt`: convergence condition to stop iteration (default: cg.rt=0.001) ## Returns a list with the following elements - **`cond`**: Weight function, scale, and other arguments choosed - **`TK`**: robustly estimated regression coefficients using Tukey's biweight - **`HB`**: robustly estimated regression coefficients using Huber weight - **`wt`**: final robust weights - **`rp`**: total number of iteration - **`s1`**: iterative changes in the sclae of residuals (AAD or MAD) ## Examples ```r require(robRatio) set.seed(4) cov1 <- matrix(c(3, 2.8, 2.8, 3), 2, 2) cov2 <- matrix(c(2.5, 0, 0, 3), 2, 2) dat1 <- MASS::mvrnorm(n=400, mu=c(100, 100), Sigma=cov1, empirical=TRUE) dat2 <- cbind(runif(100, min=96, max=104), runif(50, min=95, max=105)) dat3 <- matrix(c(103, 103.5, 104.5, 104.8, 96, 98, 94, 95), 4, 2) dat <- rbind(dat1, dat2, dat3) plot(dat) y1 <- dat[,2] x1 <- dat[,1] R0 <- lm(y1~x1) # regression by OLS o1 <- robReg(x1, y1, tp=4) # robust regression by IRLS (more robust) o2 <- robReg(x1, y1, tp=8) # robust regression by IRLS (less robust) oldpar <- par(mfrow=c(2,2)) # non-robust regression plot(dat, pch=20, main="non-robust regression") abline(R0, col="red", lwd=2) # robust regression with coloring robust weight f.o1 <- rep(1, length(x1)) f.o1[which(o1$wt < 0.8)] <- 3 f.o1[which(o1$wt < 0.5)] <- 7 f.o1[which(o1$wt < 0.2)] <- 2 f.o1[which(o1$wt == 0)] <- 8 plot(x1, y1, pch=20, col=f.o1) abline(R0, col="red", lty=3) abline(o1$TK, col="blue", lwd=2) abline(o2$TK, col="cyan", lwd=2) # robust weights (more robust) hist(o1$wt, main="tp=4(more robust)") # robust weights (less robust) hist(o2$wt, main="tp=4(less robust)") par(oldpar) ```

robReg function