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I have two continuous variables that may have nonlinear relationship. The dataset contains multiple recordings of X, each corresponding to multiple recordings of Y. The exact matching is unknown.

How Do I detect window of X corresponding to each Y?
Should I use distance correlation tests with sliding window of X?

UPDATE: X are EEG recordings. Y are sound recordings. Each EEG recording corresponds to multiple sound recordings. I want to process EEG and corresponding sound in parallel.

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    $\begingroup$ This terse, abstract description makes it difficult to understand your problem. Could you perhaps supply a small example of the data and what you intend to accomplish? $\endgroup$
    – whuber
    Feb 23 '21 at 14:51
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If I understood correctly you have observations $(x_i, y_i)_i$ from the joint distribution $p_{X,Y}$. It seems you are asking about the quantity $$\mathrm{Supp}(p_{X\mid y}) = \{ x\mid p_{X\mid Y}(x\!\mid\!y) > 0 \}$$

You should be able to estimate the joint pdf $p_{X,Y}$ of your data. This can be done via a good ol' KDE estimation or via the use of copulas. Both methods have implementations in R and python.

This however goes against Vapnik's Principle, so there must be a simpler way to estimate the support of $X\mid Y=y$ without the estimation of the entire pdf.

If your goal is to estimate a conditional distribution on complex domains such as soundwaves or images, consider using conditional generative models.

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  • $\begingroup$ That does not answer the question: How Do I detect window of EEG corresponding to each sound recording? $\endgroup$ Mar 31 '21 at 10:26

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