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This paper formalizes and extends proposals by Sir Richard Stone for adjusting initial unbalanced estimates of the components of a matrix so that they optimally satisfy accounting requirements imposed by tabular form. Stone's proposal, based on linear combinations of initial unbiassed estimates...
|a The estimation of large social account matrices /
|c R. P. Byron.
260
|a Washington, D.C. :
|b The World Bank,
|c 1978
300
|a [9 p.]
490
0
|a World Bank reprint series ;
|v no. 65
500
|a Separata de: Journal of the Royal Statistical Society, series A, vol. 141 (1978), part 3 pp. 359-367.
520
3
|a This paper formalizes and extends proposals by Sir Richard Stone for adjusting initial unbalanced estimates of the components of a matrix so that they optimally satisfy accounting requirements imposed by tabular form. Stone's proposal, based on linear combinations of initial unbiassed estimates, has many potential applications in national income accounting, input-output construction and demography, amongst other fields. Given that the Stone adjustment procedure simply represents the first-order conditions resulting from the minimization of a quadratic loss function it is possible, as is done here, to develop alternative procedures for minimizing the constrained loss function. These procedures, based on the conjugate gradient algorithm, prove to be much more efficient than the traditional solution, both in terms of time taken and storage requirements, and the optimal adjustment of very large (say 1,000 × 1,000) social account matrices becomes quite feasible. Some other minor problems are handled which relate to multiple prior estimates of cell members, and cell members for which no prior estimate exists at all. The techniques were applied to a social account matrix constructed for the Muda River district in West Malaysia and, though the results are too detailed to present here, figures are given which indicate the feasibility and usefulness of the methods.
