Confidence regions for the parameters in nonlinear regression: a preliminary survey

With reference to non-differential methods proposed in statistical literature for nonlinear confidence regions definition, Hartley's method occupies an enviable position: it is extremely easy and provides an exact (1-alpha) jointly confidence region for the unknown parameters. In the class of differential methods, of a well-known complexity and generally not exact, the pioneeristic Beale's work and the more recent differential geometry approach by Zanella are examined. After a brief description of the typical characters of the three methods, the corresponding confidence regions for a model determined by an ordinary linear differential equation with constant coefficient are compared with the aim to provide some information for a subsequent simulation.