Editorial: Fundamentals of The Theory of Sampling

Unbiased estimates for products of moments and cumulants for finite and infinite populations

“…Raghunandanan and Srinivasan (1973) give multivariate analogs of E µ r for 5 ≤ r ≤ 8 in terms of symmetric functions with tables to express these in terms of noncentral moments, and E(X − µ) r for r = 5, 6. The latter agree with Sukhatme except have −5e 3 where Sukhatme has e 2 −6e 3 in the coefficient of µ 2 3 in E(X −µ) 6 . Sukhatme's version is the correct one since g 9 n 6 is C 33 = C 3 ⊗ C 3 in the notation of Dwyer and Tracy.…”

“…For example µ 2 /(1 − n −1 ) implies µ 2.11 = µ 2.11 /(1 − n −1 ) is an UE of µ 2.11 where µ 2.11 = µ 2.11 (F ). The same method gives expectations for products of sample cross-moments and UEs for products of cross-moments for the multivariate versions of µ 2 , µ 2 , µ 3 , µ 3 , µ 4 , µ 2 2 , µ 4 , µ 5 , . .…”

“…a partition of r. We assume all partitions π are put into ascending order (1 r 1 2 r 2 • • • ). For example, we write 1 2 2 or (112) rather than 21 2 or (121).…”

One-Sided Estimating and Testing Problems for Location Models From Grouped Samples

“…The studying of statistical inference in grouped samples may be dated back to the beginning of the century and some early results may be found in (1), (2), (3), (4) and (5). (6) assembled and developed the work about the estimation of location and scale parameters.…”

Historical Survey of the Development of Sampling Theories and Practice

“…While the analysis of variance technique was being developed, another important phase of sampling theory was initiated. Combinatory analysis was applied by Professor Carver (1930) to the estimation of errors in sampling He was the founder of the Annals of Mathematical Statistics, and in the first volume of that journal he outlined his new technique. By means of the new theory, error-estimates could easily be calculated for almost any type or design of sampling, and, in conjunction with the analysis of variance technique, the general outline of sampling theory reached its final form about 1935.…”