Doctoral Dissertation Defense: Jian Zhao

Title: Some approximate confidence intervals and regions for inter-laboratory data analysis

Abstract
The problem of interest in inter-laboratory studies is statistical inference concerning a common mean by combining the data from the different laboratories. The measurements from the different laboratories exhibit different within-laboratory variances, in addition to a between laboratory variability. The one-way heteroscedastic random effects model is very often used for the data analysis. Under such a model, accurate confidence intervals are developed for the common mean using some modifications of the log-likelihood ratio statistic.  A feature of analytical measurements is that they may exhibit increasing measurement variation with increasing analyte concentrations and near-constant measurement variation at low concentration levels. A two-component measurement error model can be used to capture this feature. Such models are considered in the dissertation for data from a single laboratory and from multiple laboratories, and accurate confidence intervals are developed. Finally, a multivariate heteroscedastic one-way random effects model is taken up and two problems are addressed: improved estimation of the between-laboratory covariance matrix, and confidence regions for the common mean vector. Bootstrap methods are used for the confidence region derivation. The accuracy of the proposed methods are assessed using estimated coverage probabilities, and are also illustrated with examples.