Cross Validation and OLS Maybe a silly question: I am used to cross validating in order to tune the hyperparameters of a model (e.g., alpha and lambda in case of an elastic net).
Does it make any sense at all to talk about cross validation for an ordinary least square (OLS) model, which has no hyperparameters whatsoever? In any case, it can be useful to train the model on part of the data and test it on another data segment in order to have an unbiased estimate of its performance.
Am I talking nonsense? I'd like to have your thoughts on this matter.
 A: 
Does it make any sense at all to talk about cross validation for an ordinary least square (OLS) model, which has no hyperparameters whatsoever? 

Absolutely! One of the main goals (IMO) with any kind of model building (with the purpose of making predictions) should be minimizing generalization error and reducing overfitting, both of which are addressed by cross validation.

In any case, it can be useful to train the model on part of the data and test it on another data segment in order to have an unbiased estimate of its performance. Am I talking nonsense?

Not complete nonsense :)
To show an estimator, $\hat{\beta}$, is unbiased, one must show that $$Bias_{\beta}(\hat{\beta}) = E_{\beta}[\hat{\beta}|X] - \beta = 0$$
The solution to OLS can be shown to be:
$${\bf \widehat{\beta}_{OLS} = (X^TX)^{-1}X^Ty}$$
And the expected value of this:
$$E_{\beta}[{\bf \widehat{\beta}_{OLS}|X] = E[(X^TX)^{-1}X^Ty] = \beta}$$
Because the model form is $Y = X\beta + \epsilon$ where $\epsilon \sim N(0,I\sigma^2)$
Nowhere here is there any mention of training/testing/cross validation.
But again, one should always perform cross validation, IMO.
