Is there a name for the following process?


Say I have an absolutely continuous probability density function $f$ with compact support, and I take $k$ independent samples $x\_1,\dots,x\_k$ from $f$. Then, I let $x^\*$ be the sample for which $f(x\_i)$ is the largest, i.e. $x^\* = \arg \max\_i f(x\_i)$. My question is, is there a name for this process, and can anything be said about the distribution of $x^\*$? This basically has the effect of emphasizing the modes of $f$ more aggressively.



Choosing a sample based on where the density function is highest
If your $k$ samples are taken with replacement, then your method is a *Bootstrap estimate of the mode*. In the limit of a large number of such samples, the Bootstrap estimate coincides with the true mode.


[Bootstrapping](https://en.wikipedia.org/wiki/Bootstrapping_(statistics)) is useful when seeking the variance of a statistic such as the mode, as in your case.


