Locally quadratic log likelihood and data-based transformations

The investigation of multi-parameter likelihood functions is simplified if the log likelihood is quadratic near the maximum, as then normal approximations to the likelihood can be accurately used to obtain quantities such as likelihood regions. This paper proposes that data-based transformations of the parameters can be employed to make the log likelihood more quadratic, and illustrates the method with one of the simplest bivariate likelihoods, the normal two-parameter likelihood.