Estimation of data measured with error and subject to linear restrictions
提出一种方法，在不知道数据可靠性的情况下，对存在测量误差且需满足线性约束的观测值进行估计，并应用于美国实际GNP的支出与收入/产出估计差异的分解。
Abstract Variables are often measured subject to error, whether they are collected as part of an experiment or by sample surveys. A consequence of this is that there will be different estimates of the same variable, or, more generally, linear restrictions which the observations should satisfy but fail to. With knowledge of the variances of the various observations, it has been shown elsewhere that maximum‐likelihood estimates of the observations can be produced. This paper shows how, given a sequence of such observations, estimates can be produced without knowledge of data reliabilities. The method is applied to estimates of constant price US GNP. It suggests that 64 per cent of the discrepancy should be attributed to the expenditure estimate, with only 36 per cent going to the income/output estimate. The current method of presentation, on the other hand, places the whole of the error in the income/output estimate.