Finding local extrema of a density function using splines

I am trying to find the local maxima for a probability density function (found using R’s density method). I cannot do a simple “look around neighbors” method (where one looks around a point to see if it’s a local maximum with respect to its neighbors) as there is a large volume of data. Furthermore, it seems more efficient and generic to use something like Spline interpolation and then find the roots of the 1st derivative, as opposed to building a “look around neighbors” with fault tolerance and other parameters.

So, my questions:

  1. Given a function from splinefun, what methods will find the local maxima?
  2. Is there an easy / standard way to find derivatives of a function returned using splinefun ?
  3. Is there a better/standard way to find the local maxima of a probability density function ?

For reference, below is a plot of my density function. Other density functions I’m working with are similar in form. I should say that I am new to R, but not new to programming, so there may be a standard library or package for achieving what I need.
density function

Thanks for your help!!

Answer

What you want to do is called peak detection in chemometrics. There are various methods you can use for that. I demonstrate only a very simple approach here.

require(graphics)
#some data
d <- density(faithful$eruptions, bw = "sj")

#make it a time series
ts_y<-ts(d$y)

#calculate turning points (extrema)
require(pastecs)
tp<-turnpoints(ts_y)
#plot
plot(d)
points(d$x[tp$tppos],d$y[tp$tppos],col="red")

Attribution
Source : Link , Question Author : aaronlevin , Answer Author : Roland

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