Consistent correction of census and vital registration data

A new procedure is developed for simultaneously and consistently correcting two or more censuses and intercensal registered births and deaths. The procedure begins with a set of preliminary correction factors, which are not necessarily consistent. It then uses the mathematics of finite-dimensional vector spaces to derive an optimal set of final consistent correction factors. The optimization procedure is based on the principle that there exists in a hyperplane a unique point of minimum distance from a fixed point not in the hyperplane. For purposes of illustration, the procedure is applied to the censuses of 1970, 1975, and 1980 and intercensal registered births and deaths for the periods 1970-75 and 1975-80 for the Republic of Korea.