Construction of classical confidence regions of model parameters in nonlinear regression analyses

Abstract

Feldman-Cousins' unified approach provides an unique confidence region for parameters under estimation and assures an exact coverage for the constructed confidence region. We present a procedure to implement this approach in least-squares regression analyses. The procedure is based on a series of the most powerful likelihood-ratio tests of hypothesis using a single number as a test statistic. The procedure thereby avoids the complications of the Feldman-Cousins method arising when the number of free parameters is more than one. Applying the procedure to a case of nonlinear regression problems where the estimated parameters are not generally Gaussian distributed, we show that one has to use the procedure when the results of the regression analysis are to be carefully investigated near a boundary of the physical region.