WALD, Abraham. Sequential Tests of Statistical Hypotheses.
Beachwood: Institute of Mathematical Statistics, 1945. First edition.

Absolutely mint copy of the issue of 'Annals of Mathematical Statistics' containing Wald's groundbreaking paper. "Probability theory came of age with the advent of Kolmogorov's axiomatics in 1933 and the subsequent developments in limit theorems and stochastic processes. Statistical inference came of age with the advent of the Neyman-Pearson theory in 1933 and the subsequent formalization of hypothesis testing, estimation, and decision theory. In the present paper, Wald unified the two seemingly dissimilar areas most elegantly. To probabilists, he offered gems of new results in random walks, martingales, stochastic processes, and limit theorems. He also pointed out indirectly how they can seek probability questions from statistical inference and use the latter area as a testing ground for their abstract theorems. To statisticians, he showed that statistical inference is not just the analysis or 'significance' of an existing body of data; it also entails their entry into the very process of experimentation and continual analysis of the data as they come available. The sequential probability ratio test embodies this aspect. Wald also showed them how results from 'pure' mathematics, particularly probability theory, can be adapted to put statistical inference, in general, on stronger footing without losing sight of its practical nature." (Kotz & Johnson: Breakthroughs in Statistics). Wald's work was conceived during the summer of 1943 while he was part of the Statistical Research Group at Columbia University. His theoretical results first appeared already in September 1943, but in the form of a 'restricted' report, meaning that the Defense Department considered the results significantly important for the war effort and, therefore, decided not to disseminate them to the general public for a while. The report was 'declassified' in early 1945, thereby allowing the present paper to appear in June of that year. Interestingly enough, Wald had already in his paper 'On Cumulative Sums of Random Variables' from 1944 (also offered here), published many of the mathematical foundations of sequential procedures without any mention of the word sequential or any reference to his 1943 report, as the protocol called for.

Two mint issues of The Annals of Mathematical Statistics in original printed wrappers. 'Sequential Tests of Statistical Hypotheses' in the June issue of volume XVI, pp. 117-186. 'On Cumulative Sums of Random Variables' in September issue of volume XV, pp.283-296. Scarce in such fine condition.