You're looking for a free PDF of "Mathematical Statistics" by Jun Shao. Here's some useful information:

Unbiased estimation and the Uniformly Minimum Variance Unbiased Estimators (UMVUE). The Cramér-Rao Lower Bound and Fisher information.

The book covers a wide range of topics in mathematical statistics, including:

Neyman-Pearson lemma, uniformly most powerful (UMP) tests, and likelihood ratio tests.