Lucien Le Cam (1986), New York: Springer-Verlag, Springer Series in Statistics, xxvi + 742 pp. — DOI-10.1007/978-1-4612-4946-7
Key takeaways
Filed, not read: no lawful full text was reachable (see the history note). What follows restates the book’s own front matter (“To the Reader” and the summary of contents), which Springer serves freely, labelled as such; none of it was checked against the chapters.
- The theme, in the author’s words. The statistician faces a complex experiment ℰ = {P_θ} and looks for a known, tractable experiment ℱ close enough that procedures for ℱ transfer to ℰ “without dire consequences”. Closeness is a pseudo-distance between experiments.
- Two distances, one number. The preface says that measuring closeness by risk functions under losses bounded by one, and by how closely each experiment can be mimicked by a randomisation of the other, give distances that are “not only related, but exactly equal” (Chapter 2, Theorem 2, from Le Cam 1964). Specialised to distance zero this is the Blackwell–Sherman–Stein equivalence, which Chapter 3, Section 7 states in a form.
- Structure. Chapters 1–8 are general (experiments as vector lattices and transitions, deficiencies, likelihood-ratio distributions, sufficiency and insufficiency, contiguity, limit theorems, invariance); 9–14 develop Gaussian, Poisson and exponential-family approximation, including local asymptotic normality, global asymptotic normality and posterior convergence; 16–17 recover classical results for independent and i.i.d. observations. Chapter 15 is an aside on sums of independent variables.
- Its stance on limits. “Limit theorems ‘as n tends to infinity’ are logically devoid of content about what happens at any particular n”; the author urges reading the results as approximations.
Standing in the record
Filed on 2026-10-09 at the owner’s request, from the manuscript
bibliography of 2026-10-09 (work what-survives-translation): one of the
works the manuscript considered and dropped from its final reference list.
It is the source Torgersen’s book (LIT-778) and THEORY-156 point to for the
quantitative version of the Blackwell order: deficiency as a distance, of
which Blackwell’s equivalence is the zero case. A reading of Chapter 2 would
be the second, independent treatment THEORY-156’s promote_when asks for.