Which statistic to report for repeated cross-validation? I am doing 10 times repeated 10-fold cross-validation and now I want to report the results.
What is best practice: Report the statistics over all 100 folds or to report the statistics of the means of 10 times 10-fold CV runs? 
 A: The difference between the two should not be large. That said, Kim (2008) "Estimating classification error rate: Repeated cross-validation,repeated hold-out and bootstrap" that does present an investigation of repeated CV stipulates explicitly: "we obtain the $10$-fold CV estimates $5$ times, and take the average as the final estimate" when presenting the results of repeated CV. To that respect, one of the first widely-cited papers to suggested repeated CV, Dietterich (1998) "Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms" the description of  $5\times2$-CV is based on five iterations of two-fold cross-validation and the subsequent averaging of the 5 measurements. 
So to answer the final question: it would more reasonable to report "means of 10 times 10-fold CV runs" rather than the means of 100 folds.
A: I would tend towards reporting the statistics (including range) of the 100 folds, even though the 10 fold results are not independent. While this may not be entirely valid, it is usual for people to report the range of 10-fold results when doing one repetition of 10-fold cross-validation.
Including the range should somewhat counteract the smaller CI likely from having a greater number of (non-independent) results to report.
If you wanted to be very thorough, you could fit a random intercept model for each repeat of CV results $y_i$ to account for correlation between CV results:
$$
y_i \sim N(\mu_i, \sigma_i) \\
\mu_i \sim N(\mu_0, \tau)
$$
where $\mu_i$ is the mean for CV repetition $i$ and $\mu_0$ is the overall mean, $\sigma_i$ is the variability for an individual CV repition, and $\tau$ is the variability of CV means across repetitions.
fwiw I think this model is excessive, and examining the full results from repeated CV should allow you to find the optimal/most parsimonious model fairly accurately.
