Mathematical Sciences: Development of Calibration Curve Methods and an Investigation of Their Properties

这项研究将通过为精密仪器开发新的统计校准方法来改进测量科学。标准中有误差的校准将通过变量中误差回归问题进行检查。将通过统计模型来研究分析化学中的多变量校正问题。通过将参数和非参数方面结合在一个模型中，将提供假设检验的新的数据分析替代方案。这种半参数方法将被用来估计样本中的污染百分比并提供渐近分布。

The research will improve measurement science by developing new statistical calibration methodology for precision instruments. Calibration with errors in the standards will be examined through the errors-in-variables regression problem. Multivariate calibration problems in analytical chemistry will be studied through statistical models. New data analytic alternatives to hypothesis testing will be provided by combining parametric and nonparametric aspects in one model. This semiparametric approach will be used to estimate the percentage of contamination in a sample and provide asymptotic distributions.