Chuprov on finite exchangeability, expectation of ratios, and measures of association

AbstractThe genesis of this study is a paper of A. A. Chuprov (1916) which reveals a very early understanding and manipulation (in a dispersion-theory setting) of general finitely exchangeable random variables: a mathematically elegant approach, allied with expectations, to exchangeability. (Hitherto-known historical approaches to exchangeability wer in essence via exchangeable events.) Equally little-known consequent developments of its themes by Chuprov (1922) and his student Ya. Mordukh (1923) are then sketched. The work is notable for its mathematical precision in a statistical setting, to a degree uncharacteristic of the time; and for its remarkable technical insights. In particular, precise formulas relating to moments of the sample correlation coefficient are obtained. The concept of lack of power of statistical tests in distinguishing between exchangeable and independently distributed random variables with the same marginal distributions is clearly evident