Mathematical Methods of Statistics
Cramér (1946) — Mathematical Methods of Statistics
- Result
Chapter 28, functions of sample moments: a smooth function of sample moments is asymptotically normal with variance from the first-order expansion, under the moment conditions that make the underlying sample moments asymptotically normal.
- Use
the oldest form of O6.2's argument; the fourth-moment condition (A2) is exactly the classical condition for the second sample moment.
- Verification
Chapter 28 "Asymptotic properties of sampling distributions", §28.4 "Functions of moments" confirmed in primary text (archive.org contents scan); finite-sample companions §27.4, §27.7 (audit 5 Sep 2026).
H. Cramer, Princeton University Press, 1946. Chapter 28 (asymptotic properties of sampling distributions), functions of sample moments: the classical normal limit for smooth functions of sample moments. Registered 5 Sep 2026 from memory; section numbering unverified.
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