Statisticcal Analysis Of Dispersion Family Nonlinear Model

Dispersion family nonlinear models are a new subject of mathematical statistics . It has an important theoretical and the wide potential applications. In this dissertation, some statistics inference problems of the models are studied. Q function have been used to study the statistical diagnostics for the exponential family nonlinear models with random effects. The main content is as follows:1 First we definite the very extensive dispersion family nonlinear models. Utilizing the Fisher information matrix as the weight inner product , we present a geometric framework and two curvature measures. Based on the geometric framework, we investigated the curvature measure for the mean-shift model and obtained the Cook distance, likelihood distance, deviance function etc, diagnostic statistics in term of the curvature measures for the first time.2 For the model, the test for varying dispersion is discussed. We give the test statistic based the likelihood ratio and Score statistic for the first time. These tests are illustrated with an example.3 First, we introduced the dispersion family nonlinear models with random effects and discuses the asymptotic properties of the parametric estimation. For this model we present a geometric framework for the first time. The confidence regions for parameter and parameter subset are respectively derived from the geometric point of view. We also discuss some asymptotic properties from geometric point of view to dispersion family nonlinear models with random effects.4 For the exponential family nonlinear models with random effect, we utilized the latent variable model and Q function to study the diagnostics and local influence problem for the first time. For achieving the parameter estimation, the Gibbs sampler and the Metropolis-Hastings algorithm are utilized.