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I calculated the quantiles for an Epanechnikov kernel which I'm using to estimate the density of a sample. What I need is to find the sample quantiles knowing that it is composed of many Epanechnikov kernels. Is there a way to calculate at wich data points the different quantiles are using the kernel inverse CDF formula?

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    $\begingroup$ If you mean that you have a density function expressed as a linear combination of Epanechnikov densities and you wish to compute its quantiles directly using the inverse CDF, the answer is no in general. (Conceivably some special configurations of data--equal spacing comes to mind--could be amenable to such an approach.) You're best off integrating your density using the CDF of the kernels and numerically finding its quantiles. $\endgroup$
    – whuber
    Jan 28 '11 at 16:45
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    $\begingroup$ This paper may be useful as a "structural" guide to what you want to do, but you will need to adapt it to the particular distribution you used. It uses a normal mixture, rather than a Epanechnikov mixture $\endgroup$ Jan 29 '11 at 16:41

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