For finite sample sizes, more than two solutions are possible depending upon the model. For the normal homoscedastic model, there are exactly two solutions for all sample sizes. Development of starting values for iterative solution of the contour method equations. This is accomplished by replacing the equations by the lowest order terms in their asymptotic expansions and solving the simplified approximating equations. Implementation of the contour method and assessment of its behavior for small sample sizes.
Simulation is used to obtain achieved coverage levels that are compared with nominal levels.
We also compute the coverage probabilities achieved by using the starting values described in item 3 above. Two additional skew families, the lognormal and reciprocal gamma, are included by transformation to the normal and gamma, respectively. Results indicate that asymptotic confidence limits computed from the contour method yield coverage probabilities that match the nominal levels to within a percentage point or two, and that convergence to nominal levels is quite rapid with increasing sample sizes. Using the starting values as final values achieves a coverage that is somewhat inferior to the final iterative solution for small sample sizes. Thus, full iterative solution will usually be worth the computational effort unless the sample sizes are large.