Discussion of 'The Contributions of Robert A. Wijsman to Sequential Analysis' by Adam T. Martinsek

摘要

Adam has written a masterly review of all of Bob's work on sequential analysis. One can only add a few technical or personal details that may be of interest. I read the three papers of Bob on sequential probability ratio tests (SPRTs) for simple hypotheses about i.i.d. random variables when I had just begun my doctoral research and was trying to solve a problem given to me by my adviser, Harikinkar Nandi. While trying to solve Nandi's problem, I had come across an article by Lindley (1953) and its review in the Mathematical Reviews by Wolfowitz (1954). Probably both had been pointed out to me by Nandi. Wolfowitz had a pretty argument that reduced Lindley's long and a bit incomplete proof to a page. I couldn't solve Nandi's problem till much later, in 1964, but I wrote a decision theoretic proof of some of Bob's results in CSA Bulletin (1961). I never found out if Bob had ever read my proof (Ghosh, 1961) of his results on the existence of SPRTs for given α, β (α + β < 1), "monotonicity," and optimality when the restriction to finite ASN is dropped.