Applying statistical test on model residuals

Hi,

My query is not directly related to R; however, I hope to gain some
insight from the experienced statisticians here regarding a
statistics-related question.


Typically, to assess model adequacy, we apply various statistical
tests—such as tests of randomness, normality tests, etc.—directly to
the estimated residuals. I wonder to what extent such procedures are
theoretically valid, since these tests are not being applied to the
raw data generated from the underlying physical process, but rather to
quantities that are themselves estimated or derived from a fitted
statistical model.


Is there any research paper/text book available to discuss this in detail?

Any insight would be very helpful.

Thanks for your time.