Theses and Dissertations at Montana State University (MSU)
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/732
Browse
6 results
Search Results
Item Anderson-Darling Regression with two examples from biofilm engineering(Montana State University - Bozeman, College of Letters & Science, 1997) Daly, Don SimoneItem Estimation of cumulative totals(Montana State University - Bozeman, College of Letters & Science, 1976) Shaffer, Charles EdwardItem Numerical solution of nonlinear regressions under linear constraints(Montana State University - Bozeman, College of Agriculture, 1975) Yeh, Ning-ChiaItem Using incomplete multivariate data to simultaneously estimate the means(Montana State University - Bozeman, College of Letters & Science, 1979) Hinkins, Susan MarieItem Ratio estimation in randomized response designs(Montana State University - Bozeman, College of Letters & Science, 1974) Peterson, Reider SverreItem Robust methods for multivariate linear models with spectral models for scatter matrices(Montana State University - Bozeman, College of Letters & Science, 2004) Hyde, Scott Kohler; Chairperson, Graduate Committee: Robert J. BoikThe main goal of this dissertation is to present extensions to the robust estimation of multivariate location and scatter. These extensions include the estimation of structured scatter matrices embedded in a multivariate fixed effects model. Two different kinds of robust estimators are investigated. The first is based on Maronna's M-estimators of multivariate location and scatter (Maronna 1976). The second is a multivariate extension of the S-estimators introduced by Rousseeuw and Yohai (1984). In addition, asymptotic distributions of the estimators are derived from an estimating function approach. The sandwich estimator of the asymptotic variance is given, coupled with second order corrections to the bias of the estimators. Two different data sets are used to illustrate the techniques of the dissertation. A comparison of the new algorithms to Ruppert's SURREAL algorithm is made for each example. Models are fit to illustrate the flexibility of the new estimators. In addition, the sandwich estimate of the asymptotic variance is given for the examples. Simulations are performed evaluating the effectiveness of the estimators.