The trade off will be how certain you are about your parameter estimates since as the cetral limit theorem states the confidence increases with n. So either you are relatively certain about the parameters that result from the training or about those from the test data.

  You can have a look here. "There are two competing concerns: with less training data, your parameter estimates have greater variance. With less testing data, your performance statistic will have greater variance."

Thus there will always be some trade off and I gues there is no general rule of thump. The only rule of thump I can think of is not using an extreme ratio as you describe since it leads to useless results either of training or testing.

Using terminology of your question, with small training samples you are validating a weak hypothesis. On the other hand, using small test data makes you uncertain wether your strong hypothesis is true. Both is not very satisfying so you usually want to balance both concerns.

As the sample decreases the variance error of your estimates will increase. Thus the trade off will be how certain you are about your parameter estimates - either you are relatively certain about the parameters that result from the training or about those from the test data. You can have a look here.

Using terminology of your question, with small training samples you are validating many weak hypothesis. On the other hand, using small test data makes you uncertain wether your strong hypothesis is true. Both is not very satisfying so you usually want to balance both concerns by deviding the data less extreme, e.g. deviding by 70/30 or so.

The trade off will be how certain you are about your parameter estimates since as the cetral limit theorem states the confidence increases with n. So either you are relatively certain about the parameters that result from the training or about those from the test data.

You can have a look here. "There are two competing concerns: with less training data, your parameter estimates have greater variance. With less testing data, your performance statistic will have greater variance."

Thus there will always be some trade off and I gues there is no general rule of thump. The obly rule of thump I can think of is not using an extreme ratio as you describe since it leads to useless results either of training or testing.

The trade off will be how certain you are about your parameter estimates since as the cetral limit theorem states the confidence increases with n. So either you are relatively certain about the parameters that result from the training or about those from the test data.

You can have a look here. "There are two competing concerns: with less training data, your parameter estimates have greater variance. With less testing data, your performance statistic will have greater variance."

Thus there will always be some trade off and I gues there is no general rule of thump. The only rule of thump I can think of is not using an extreme ratio as you describe since it leads to useless results either of training or testing.

Using terminology of your question, with small training samples you are validating a weak hypothesis. On the other hand, using small test data makes you uncertain wether your strong hypothesis is true. Both is not very satisfying so you usually want to balance both concerns.