obtain global maximum of a fitted smoothing spline from R function 'smooth.spline'

Question

I smoothed my data using smooth.spline(x,y) and now I want to calculate the mode or maximum of smoothed curve.

x <- vect.1
y <- vect.2
plot(x, y, type = 'l')
smth <- smooth.spline(x, y)
lines(smth, col = 'red', lwd = 2)

My current approach is simply to look up the x which gives me the maximum y which is not so accurate. Is there a better way for doing this?

Answer 1

psmth <- predict(smth, x= seq(1,100, by=0.1) )
mode_psmth <- psmth$y[ which.max( psmth$y ) ]

Or even:

mode_psmth <- max(psmth$y)

If this is not "sufficiently accurate", then please explain why.