| Title | Author(s) | Legal Free Access | |-------|-----------|-------------------| | Mathematical Statistics | P. R. Vittal | No free PDF; buy used or library | | Introduction to Mathematical Statistics (7th ed.) | Hogg, McKean, Craig | Partial via Google Books | | All of Statistics | Larry Wasserman | Free PDF from author’s website (legit) | | Mathematical Statistics with Applications | Wackerly, Mendenhall, Scheaffer | Older editions on Internet Archive (borrow) | | Probability and Statistics | DeGroot & Schervish | Sample chapters free via publisher |
: Random variables, mathematical expectations, variance, and characteristic functions. | Title | Author(s) | Legal Free Access
When the alternative is composite but has a monotone likelihood ratio (MLR) in a statistic (T(X)), the test that rejects for large values of (T) is UMP. The formalizes this for one‑parameter exponential families. When the alternative is composite but has a
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The book is typically divided into two main sections:
The provides a lower bound for the variance of any unbiased estimator (\hat\theta): [ \operatornameVar(\hat\theta) \ge \frac1I(\theta) \quad\textwhere I(\theta)=E!\left[\left(\frac\partial\partial\theta\log f(X;\theta)\right)^2\right] ] If an estimator attains this bound, it is efficient .