Comparison of asymptotic confidence sets for regression in small samples

In case of small samples, asymptotic confidence sets may be inaccurate, with their actual coverage probability far from a nominal confidence level. In a single framework, we consider four popular asymptotic methods of confidence estimation. These methods are based on model linearization, F-test, likelihood ratio test, and nonparametric bootstrapping procedure. Next, we apply each of these methods to derive three types of confidence sets: confidence intervals, confidence regions, and pointwise confidence bands. Finally, to estimate the actual coverage of these confidence sets, we conduct a simulation study on three regression problems. A linear model and nonlinear Hill and Gompertz models are tested in conditions of different sample size and experimental noise. The simulation study comprises calculation of the actual coverage of confidence sets over pseudo-experimental datasets for each model. For confidence intervals, such metrics as width and simultaneous coverage are also considered. Our comparison shows that the F-test and linearization methods are the most suitable for the construction of confidence intervals, the F-test – for confidence regions and the linearization – for pointwise confidence bands.