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

该研究将通过开发新的精密仪器统计校准方法来改进测量科学。校正误差的标准将通过误差在变量回归问题进行检查。分析化学中的多变量校准问题将通过统计模型进行研究。通过在一个模型中结合参数和非参数方面，将提供新的数据分析替代假设检验。这种半参数方法将用于估计样本中污染的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.