Details

Autor(en) / Beteiligte

• Chance, Beth L

Titel

Behavior characterization and estimation for general hierarchical multivariate linear regression models

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

1994

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• In many types of experimental research, data are hierarchical in nature, with several variables measured at different levels. To best understand the underlying phenomena, we need to be able to specify the variables at the separate levels and estimate them accordingly. In this thesis we are concerned with the sensitivity of these estimates to the distributional assumptions at each level in the hierarchy. We extend a theoretical result for convolutions to our hierarchical models. We show that densities can be divided into three classes, and that the class membership determines the posterior behavior for location parameters in the presence of extreme observations. We extend this theory to models with more than two levels, multidimensional parameters, and scale parameters. Our result encompasses earlier results on "what-if" asymptotics and bounded influence in Bayesian analysis. In this thesis we also implement a Gibbs Sampling algorithm for estimation in our hierarchical multivariate linear regression model that includes a representative density from each of the three classes. Our implementation allows multivariate Laplace and t densities at each level, as well as independent Laplace and t densities at the data level.