# Kernel regression Calculates a kernel regression estimate (univariate or multivariate). ```r kreg(x, y, bandwidth = NULL, grid = TRUE, kernel = "biweight", product = TRUE, sort = TRUE) ``` ## Arguments - `x`: n x d matrix, data - `y`: n x 1 vector, responses - `bandwidth`: scalar or 1 x d, bandwidth(s) - `grid`: logical or m x d matrix (where to calculate the regression) - `kernel`: text string, see `kernel.function` - `product`: (if d>1) product or spherical kernel - `sort`: logical, TRUE if data need to be sorted ## Details The estimator is calculated by Nadaraya-Watson kernel regression. Future extension to local linear (d>1) or polynomial (d=1) estimates is planned. The default bandwidth is computed by Scott's rule of thumb for kde (adapted to the chosen kernel function). ## Returns List with components: - **x**: m x d matrix, where regression has been calculated - **y**: m x 1 vector, regression estimates - **bandwidth**: bandwidth used for calculation - **df.residual**: approximate degrees of freedom (residuals) - **rearrange**: if sort=TRUE, index to rearrange x and y to its original order. ## Author(s) Marlene Mueller ## See Also `kernel.function`, `convol`, `kde` ## Examples ```r n <- 1000 x <- rnorm(n) m <- sin(x) y <- m + rnorm(n) plot(x,y,col="gray") o <- order(x); lines(x[o],m[o],col="green") lines(kreg(x,y),lwd=2) ## two-dimensional n <- 100 x <- 6*cbind(runif(n), runif(n))-3 m <- function(x1,x2){ 4*sin(x1) + x2 } y <- m(x[,1],x[,2]) + rnorm(n) mh <- kreg(x,y)##,bandwidth=1) grid1 <- unique(mh$x[,1]) grid2 <- unique(mh$x[,2]) est.m <- t(matrix(mh$y,length(grid1),length(grid2))) orig.m <- outer(grid1,grid2,m) par(mfrow=c(1,2)) persp(grid1,grid2,orig.m,main="Original Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) persp(grid1,grid2,est.m,main="Estimated Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) par(mfrow=c(1,1)) ## now with normal x, note the boundary problem, ## which can be somewhat reduced by a gaussian kernel n <- 1000 x <- cbind(rnorm(n), rnorm(n)) m <- function(x1,x2){ 4*sin(x1) + x2 } y <- m(x[,1],x[,2]) + rnorm(n) mh <- kreg(x,y)##,p="gaussian") grid1 <- unique(mh$x[,1]) grid2 <- unique(mh$x[,2]) est.m <- t(matrix(mh$y,length(grid1),length(grid2))) orig.m <- outer(grid1,grid2,m) par(mfrow=c(1,2)) persp(grid1,grid2,orig.m,main="Original Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) persp(grid1,grid2,est.m,main="Estimated Function", theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5) par(mfrow=c(1,1)) ```

kreg function