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From the book "Data Analysis and Data Mining" by Adelchi Azzalini and Bruno Scarpa, page 206:

Such a low percentage and the small absolute value suggest using cross-validation to trade off bias and variance. We assessed the performance of different models by 10-fold cross-validation, using the same random partition for all methods. To compare the actually observed data, we predicted each of the 10 parts using the best model fitted by using the other parts, thus avoiding having to divide the data set into training and validation sets. We typically also used inner cross-validation to choose a model within each class.

What is inner cross validation?

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I think the authors just mean they did cross-validation to choose models within each fold of the first (outer) cross-validation. That's what I would usually call "nested cross-validation".

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On each of the 10 folds, there was a model selection performed separately, for example for feature selection. This cross-validation on the folds is then called inner crossvalidation. This has to be done to avoid a bias when using cross-validation to balance the model (like in this case).

For more information, see the wikipedia-entry on cross validation (especially chapter Limitations and misuse): https://en.wikipedia.org/wiki/Cross-validation_%28statistics%29

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