Geometry of exponential type regression models and asymptotic inference (Q1319144)

Exponential type regression models with the density function: \[ f(y,\theta, \sigma^ 2) = \exp \{-b(y, \theta)/ \sigma^ 2 + c(y, \sigma^ 2)\} \] are considered, where the components of the observed vector \(y = (y_ 1, \dots, y_ n)\) are independent, \(\theta = (\theta_ 1, \dots, \theta_ n)\) is the natural parameter, which is always associated with a \(p \times 1\) vector of unknown parameters \(\beta\) by \(\theta = \theta(\beta)\), \(\beta\) varies in a compact set of \(R^ n\), \(\sigma^ 2\) is the dispersion parameter, \[ b(y,\theta) = \sum_ t b_ t (y_ t, \theta_ t), \] and \(b_ t (\cdot, \cdot)\) and \(c(\cdot, \cdot)\) are known functions. The stochastic expansions relating to the estimate are derived. The biases and the covariances related to the estimate may be calculated based on the expansions.