Hat Matrix of a Smoother
Compute the hat matrix or smoother matrix, of ‘any’ (linear) smoother, smoothing splines, by default.
hatMat(x, trace= FALSE,
pred.sm = function(x, y, ...)
predict(smooth.spline(x, y, ...), x = x)$y,
...)x |
numeric vector or matrix. |
trace |
logical indicating if the whole hat matrix, or only its trace, i.e. the sum of the diagonal values should be computed. |
pred.sm |
a function of at least two arguments |
... |
optionally further arguments to the smoother function
|
The hat matrix H (if trace = FALSE as per default) or
a number, tr(H), the trace of H, i.e.,
sum(i) H[i,i].
Note that dim(H) == c(n, n) where n <- length(x) also in
the case where some x values are duplicated (aka ties).
Martin Maechler maechler@stat.math.ethz.ch
Hastie and Tibshirani (1990). Generalized Additive Models. Chapman \& Hall.
smooth.spline, etc.
Note the demo, demo("hatmat-ex").
require(stats) # for smooth.spline() or loess()
x1 <- c(1:4, 7:12)
H1 <- hatMat(x1, spar = 0.5) # default : smooth.spline()
matplot(x1, H1, type = "l", main = "columns of smoother hat matrix")
## Example 'pred.sm' arguments for hatMat() :
pspl <- function(x,y,...) predict(smooth.spline(x,y, ...), x = x)$y
pksm <- function(x,y,...) ksmooth(sort(x),y, "normal", x.points=x, ...)$y
## Rather than ksmooth():
if(require("lokern"))
pksm2 <- function(x,y,...) glkerns(x,y, x.out=x, ...)$est
## Explaining 'trace = TRUE'
all.equal(sum(diag((hatMat(c(1:4, 7:12), df = 4)))),
hatMat(c(1:4, 7:12), df = 4, trace = TRUE), tol = 1e-12)
## ksmooth() :
Hk <- hatMat(x1, pr = pksm, bandwidth = 2)
cat(sprintf("df = %.2f\n", sum(diag(Hk))))
image(Hk)
Matrix::printSpMatrix(as(round(Hk, 2), "sparseMatrix"))
##---> see demo("hatmat-ex") for more (and larger) examplesPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.