Continuing with posts on E.S. Pearson in marking his birthday:
Egon Pearson’s Neglected Contributions to Statistics
by Aris Spanos
Egon Pearson (11 August 1895 – 12 June 1980), is widely known today for his contribution in recasting of Fisher’s significance testing into the Neyman-Pearson (1933) theory of hypothesis testing. Occasionally, he is also credited with contributions in promoting statistical methods in industry and in the history of modern statistics; see Bartlett (1981). What is rarely mentioned is Egon’s early pioneering work on:
(i) specification: the need to state explicitly the inductive premises of one’s inferences,
(ii) robustness: evaluating the ‘sensitivity’ of inferential procedures to departures from the Normality assumption, as well as
(iii) Mis-Specification (M-S) testing: probing for potential departures from the Normality assumption.
Arguably, modern frequentist inference began with the development of various finite sample inference procedures, initially by William Gosset (1908) [of the Student’s t fame] and then Fisher (1915, 1921, 1922a-b). These inference procedures revolved around a particular statistical model, known today as the simple Normal model:
Xk ∽ NIID(μ,σ²), k=1,2,…,n,… (1)
where ‘NIID(μ,σ²)’ stands for ‘Normal, Independent and Identically Distributed with mean μ and variance σ²’. These procedures include the ‘optimal’ estimators of μ and σ², Xbar and s², and the pivotal quantities:
(a) τ(X) =[√n(Xbar- μ)/s] ∽ St(n-1), (2)
(b) v(X) =[(n-1)s²/σ²] ∽ χ²(n-1), (3)
where St(n-1) and χ²(n-1) denote the Student’s t and chi-square distributions with (n-1) degrees of freedom. Continue reading →
