Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors
Confidence Regions for Random-Effects Calibration Curves With Heteroscedastic Errors
复制标题
具有异方差误差的随机效应校准曲线的置信区域
作者：
D. Bhaumik;R. Gibbons
我们构造随机效应校准曲线模型的置信区间。一个示例应用是分析化学数据的分析，其中校准曲线包含q个实验室中每个实验室中已知浓度x的几个值的测量值y。在本设计中，实验室被视为随机效应，允许校准曲线的截距和斜率具有实验室特定值。在这里，我们（a）为分析化学中常见的异方差数据类型绘制适当的实验室间校准曲线;（B）当q′个实验室提供相应的测量浓度Y1，Y2，.，Yq′时，计算未知真实浓度X的点估计值（即，用于校准模型的原始q个实验室的子集，其中1 ≤ q′ ≤ q）;（c）计算估计值的渐近均值和方差;（d）构建X的置信区域。然后，我们说明了使用模拟和典型的实验室间校准数据的方法。一般方法的其他相关应用突出。
We construct confidence bounds for a random-effects calibration curve model. An example application is analysis of analytical chemistry data in which the calibration curve contains measurements y for several values of known concentration x in each of q laboratories. Laboratory is considered a random effect in this design, and the intercept and slope of the calibration curve are allowed to have laboratory-specific values. Here we (a) develop an appropriate interlaboratory calibration curve for heteroscedastic data of the type commonly observed in analytical chemistry; (b) compute a point estimate for an unknown true concentration X when corresponding measured concentrations Y1,Y2,…, Yq′ are provided from q′ laboratories (i.e., a subset of the original q laboratories used to calibrate the model, where 1 ≤ q′ ≤ q); (c) compute the asymptotic mean and variance of the estimate; and (d) construct a confidence region for X. We then illustrate the methods are using both simulated and typical interlaboratory calibration data. Other relevant applications of the general approach are highlighted.