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I am analysing polymorphisms distribution data from Next Generation Sequencing data using Kernel density estimation (KDE).

However I would like to know if this method permit an unbiased comparisons, i.e.: Does KDE normalise the distribution?

The literature about this is scarce.

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    $\begingroup$ No. There is unlikely to be literature on this because there is almost nothing to say. Kernel density estimates are smoothings of the data, and broadly speaking if a distribution is skewed or long-tailed or whatever then the kernel density estimate will be similar. Regardless of what you mean by normalise or standardise, doing that before a kernel density estimate would be a separate step and kernel density estimation doesn't do it. $\endgroup$
    – Nick Cox
    Commented Mar 24, 2021 at 12:01

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Kernel density estimates are smoothings of the probability distribution. Broadly speaking, if a distribution is skewed or long-tailed or whatever, then the kernel density estimate will be similar.

Regardless of what you mean by normalise or standardise, doing that before a kernel density estimate would be a separate step; and kernel density estimation doesn't do it.

On the latter, many meanings of normalise and standardise boil down to linear scalings, say that the data now lie in $[0, 1]$ or have mean $0$ and SD $1$. Such linear scalings don't change the shape of the distribution. On the other hand, non-linear transformations such as square roots or logarithms will change the shape of the distribution.

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  • $\begingroup$ Thank you so much. It was very helpful your answer and It cleared me the idea about KDE $\endgroup$
    – Adrián P.L.
    Commented Mar 24, 2021 at 15:26

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