Statistical Analysis Of Exponential Family Nonlinear Models And Linear Models With AR(1) Errors

Exponential family is the most commonly used family in statistics, which include many families such as normal?Poisson and Gamma family. A number of authors have been concerned about exponential family nonlinear models. In 1986, R.D.Cook proposed differential geometry to assess local influence of minor perturbations of linear statistical models. Poon and Poon(1999) constructed a conformably invariant curvature , the conformal normal curvature, for the same purpose. In this paper, we introduce the estimation and algorithm o f p arameter and some diagnostic statistics. We deduce the computation formula of curvature and conformal normal curvature for four perturbations of models.Tn ordinary regression analysis, random errors are assumed to satisfy the Gauss-Markov conditions: the random errors are mutually independent, have mean zero and homogeneous variances. However, in some situations, models are hard to satisfy these assumptions at the same time. We meet a number of random errors with serial correlation and heteroscedasticity in practical problems. The rationality of these assumptions for random errors is doubtable. Therefore, it is necessary to test for correlation and heteroscedasticity in regression, which is an important step of dealing with regression problems and plays an important role in theory and practice. In this paper, we introduce the estimation and its prosperities of parameters of linear regression models with AR(1) errors and study its test for correlation and heteroscedasticity and statistical diagnostics based on case deleted models.