A good book on Statistical Inference? Anyone can suggest me one or more good books on Statistical Inference (estimators, UMVU estimators, hypothesis testing, UMP test, interval estimators, ANOVA one-way and two-way...) based on rigorous probability/measure theory?
I've checked some classical books on this topic but apparently all start from scratch with an elementary probability theory.

There's the book by Morris de Groot, and one by Bernard Lindgren.  Both have bland titles that I don't remember.  I think the former might be "Probability and Statistics" and the latter "Statistical Inference" or something like that.
Lindgren's book contains a proof that the location-scale family of Cauchy distributions admits no coarser sufficient statistic than the order statistic (i.e. an i.i.d. sample sorted into increasing order); maybe that's not a crucial thing but it's something you find frequently asserted but seldom proved, so it stands out in my mind.
Both books cover the topics you've mentioned, although they don't assume you've had measure theory.
Since you mention ANOVA, let me add that if you want to understand the theory, you should know things like the (finite-dimensional) spectral theorem, the singular value decomposition, etc.  Many books treat ANOVA and regression without that, so you won't learn why the sampling distributions of test statistics are what they are, etc.  I'm not sure which book to recommend for this right now.....
