Regression Analysis, Nonlinear or Nonnormal: Simple and Accurate p Values from Likelihood Analysis

We develop simple approximations for the p values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution; computer iteration then gives confidence intervals. Both frequentist and Bayesian versions are given. The approximations are derived from recent developments in likelihood analysis and have third-order accuracy. Also, for very small and medium-sized samples, the accuracy can typically be high. The likelihood basis of the procedure seems to provide the grounds for this general accuracy. Examples are discussed, and simulations record the distributional accuracy.