Testing Statistical Hypotheses: Volume I (sprin... -

When UMP tests do not exist, Lehmann introduces restrictions like unbiasedness and invariance to narrow the search for optimal procedures.

Lehmann’s work transformed statistics from a collection of ad-hoc methods into a structured mathematical discipline. By utilizing the Neyman-Pearson Lemma as a cornerstone, Volume I establishes why certain tests are mathematically "best." Audience and Pedagogy Testing Statistical Hypotheses: Volume I (Sprin...

Much of the theory is built upon the properties of exponential families, providing a unified framework for normal, binomial, and Poisson distributions. When UMP tests do not exist, Lehmann introduces