Robust multivariate estimation and variable selection in transportation and environmental engineering

Poor data quality is a recurring problem in observational data. We present a robust method called the multivariate L2 error (ML2E) that is used to estimate the source profiles matrix in an environmental engineering research area called receptor modeling, under non-homogenous or faulty data. We study asymptotic efficiency of the ML2E relative to a least squares method, and present simulation studies under different contamination conditions of the error distribution.; Before implementation, the ML2E is adjusted by a weight called c. We show that for large values of c, the ML 2E has similar properties to a least squares method, which is not robust in the case of heavy tailed errors. Inversely, with small values of c, the ML2E is more efficient than least squares in the case of heavy tailed errors, but less efficient than least squares in the case of normal errors. The asymptotic properties are used to suggest strategies for choosing the weight c. A simulation is presented in order to illustrate the robustness of the ML2E when there is a contamination in the mean rather than the errors.; We also study variable selection algorithms using real pollution data from the Texas Natural Resources Conservation Commission (TNRCC). Based on this study, we suggest a modified algorithm using a combination of current receptor modeling algorithms.; A special application of the techniques used in receptor modeling arose through research and consultation at the Texas Transportation Institute (TTI). We present an intuitive justification for applying the ML2E to Origin-Destination (OD) estimation. Asymptotic theorems justify the application of the ML2E to an Automatic Vehicle Identification (AVI) data set from San Antonio, Texas. The OD estimation borrows techniques from receptor modeling when two vehicle traffic ramps are systematically missing.; We close the thesis by addressing a statistical solution to an archiving problem arising from work with real-time Intelligent Transportation Systems (ITS) data.