Constrained Expected Likelihood Estimates of Precisions using Grubbs' Technique for TWO Measurement Method

The data under consideration consist of measurements performed on each of n items by two measurement methods. The problem is to obtain estimates of the measurement random error variance for each method. This problem has common application in nuclear materials safeguards, as is discussed in [1]. Grubbs [2] proposed a method of estimating these parameters. The estimators are given in Section 2. Unfortunately, when the product variance, (variance of true values of items being measured), is large relative to the measurement error variances, the estimate of one of these error variances is negative with high probability [3]-[6]. In the event that one of the estimates in question is negative, altered estimates of the parameters have been proposed by Thompson [7]. These estimators are given in Section 3. The estimate of one of the parameters is zero. Since some workers are hesitant to report zero values for variance components, the purpose of this paper is to present other estimators of the parameters that will always provide positive non-zero estimates. These estimators, and the basis for them, are given in Section 4. In Section 5, examples are given, and in Section 6, it is suggested that the estimation principle involved may be applied in general, even when Grubbs few summarizing comments are given in Section 7. 1 related estimates are all positive. A