The power of the likelihood ratio test of location in nonlinear regression models

The Likelihood Ratio Test statistic, T, is considered for the hypothesis H: θ = θ₀against A: θ ≠ θ₀in the nonlinear regression model y = f(x, θ) + 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.