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Yes, it makes complete sense in certain cases to examine the density of time-series, especially after mean-centring the original series. This relates directly to the concept of density forecasting and providing probabilistic forecasts of our continuous variables in the form of predictive densities functions. A famous reference on the matter is Gneiting et al....

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You're right that effect size statistics for nonparametric tests usually can't be expressed in terms of variance explained. Spearman correlation is equivalent to Pearson correlation on the ranks of the data. I suppose you could convert this, by squaring rho, to "variance of the ranks of y explained by the ranks of x", but I suspect relying the audience to ...

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As you already mentioned the Kruskal-Wallis test is a test of significance based on the ranks. In my opinion however, plotting the ranks isn't really that helpful for the reader in order to understand the underlying response variable. Instead, what I would do is to plot the individual data points (including the median for descriptive purposes) plus the ranks ...

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I'd recommend considering whether you actually need a correlation per se. If you're interested in the extent to which responses on your continuous variable differ across the levels of your dichotomous variable, you could just do a Mann-Whitney U test (analogous to doing a t-test for parametric data). Some background and implementation in SPSS: https://...

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This is the analogue when you have to sum over a continuum. If you were to do the sum over all of the integers, it makes sense to write a sum over the integers. You can write the infinite sum as a limit of a sequence of partial sums. Fourier series do this. $$\sum_{\mathbb{Z}}$$ However, it doesn’t make sense to talk about a sequence of partial sums for \$\...

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If you want to report the median of differences and the confidence interval for this statistic, then that's what you should do. For data that are discrete with few levels, there may not great method for doing this, but I'll present a couple of methods in R below. For these data, the median is 0 and reasonable 95% confidence limits might be -1 and 0. Note ...

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I find Thomas's answer very detailed, but I will nevertheless add a couple things to it: Since random forest models already select features, is it possible to gain much by such a method? You could have some gains from feature selection in cases of highly correlated features and when having many unimportant features. Many high correlated features might ...

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A standard deep neural network (DNN) is, technically speaking, parametric since it has a fixed number of parameters. However, most DNNs have so many parameters that they could be interpreted as nonparametric; it has been proven that in the limit of infinite width, a deep neural network can be seen as a Gaussian process (GP), which is a nonparametric model [...

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I have a feeling that you're looking for piecewise SEM, as I've heard it mentioned with reference to Pearl in the past. It is literally sequences of regressions, with some graph theory to tie things together. There are also distribution free estimators of typical SEM models though (though they don't really perform any better than ML with robust variance ...

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