@vucko gave me excellent answer on my question, unfortunately using Mathematica code. I'm trying to rewrite it in R and I'm lost in R functions providing kernel density estimation.

I have bivariate dataset with more than 46,000 rows (so I am also looking for a high performance solution--@vucko's solution is very time consuming). I would like to apply kernel density estimation and decide if some point lies in area with some density estimation level (confidence level respectively).

kernel estimate

@vucko in his answer selected two groups. I need only to know if some point lies in the green group or not. And that should be done with R.

I experimented with kde and bkde2D functions but they don't provide me desired functionality as Mathematica SmoothKernelDistribution. Can you please me show the direction? For normal distribution I found the ellipse function which approximated data with some confidence level and used inside.owin function.

  • $\begingroup$ You might try the feature package. $\endgroup$
    – Wayne
    Commented Mar 14, 2012 at 18:19
  • $\begingroup$ Feature featureSignif produces the same as bkde2D- fhat matrix which I don't know, how to use... $\endgroup$
    – matejuh
    Commented Mar 14, 2012 at 19:45
  • $\begingroup$ Some people find that SmoothKernelDistribution goes quite quickly; I have found it will take a few seconds with $10^4$ points. See the response and comments at mathematica.stackexchange.com/a/2967. $\endgroup$
    – whuber
    Commented Mar 14, 2012 at 22:19

1 Answer 1


I think the hdrcde package does what you want. Here is something quite similar to your example:

n <- 23000
x <- c(runif(n,0,1),runif(n,0,.6))
y <- c(x[1:n], 7*x[n+(1:n)]) + rnorm(n)
y <- (y-min(y))/(max(y)-min(y))

den <- hdr.boxplot.2d(x,y,prob=.30,h=c(2.,2),pch=".",pointcol="red")
j <- (den$fxy > den$falpha)

That will give you the points within the contour of 30% probability. It is very fast, even with 46000 observations.

  • $\begingroup$ The prob=0.30 argument controls the confidence area. $\endgroup$ Commented Mar 14, 2012 at 23:26
  • $\begingroup$ I gives me strange result. I don't know, how to control the confidence area. My result with straight use of your code on my data looks like: wrong result What I actually needs is when I have some data with kernel density estimation like: kernel And if I have point x[100000,3000] I would like to decide if it lies in azure confidence level or bigger. $\endgroup$
    – matejuh
    Commented Mar 14, 2012 at 23:30
  • $\begingroup$ Thanks for response @Rob Hyndman, sorry I add comment before I finished it... I know that prob controls the confidence area, but it has very wheard behaviour on my data. $\endgroup$
    – matejuh
    Commented Mar 14, 2012 at 23:33
  • $\begingroup$ Most likely you need to modify the bandwidth for the density estimation. That is controlled by the h argument. $\endgroup$ Commented Mar 14, 2012 at 23:33
  • $\begingroup$ Is there any automatic way how to do it? When I used it with bkde2D I just tested some values. $\endgroup$
    – matejuh
    Commented Mar 14, 2012 at 23:44

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