(in Theory and Methods)

The Power of the Likelihood Ratio Test of Location in Nonlinear Regression Models

A. R. Gallant
Journal of the American Statistical Association, Vol. 70, No. 349. (Mar., 1975), pp. 198-203.


The Likelihood Ratio Test statistic, T, is considered for the hypothesis H: q = q0 against A: q ¹ q0 in the nonlinear regression model y = f(x, q) + e with normal errors and unknown variance. The distribution function of a random variable X such that n·(T - X) converges in probability to zero is derived. Using X to approximate T, the power of the Likelihood Ratio Test is tabulated for selected sample sizes and departures from the null hypothesis. The adequacy of the approximation of T by X is investigated in a Monte-Carlo study.