Improving Likelihood-Ratio-Based Confidence Intervals for Threshold Parameters in Finite Samples

We propose an improved method for constructing likelihood-ratio-based confidence intervals for threshold parameters in threshold regressions. Related methods have been extensively developed in the literature and are asymptotically valid. However, their performance in finite samples is not satisfactory. We suggest two modifications to the standard inverted likelihood ratio approach. First, we consider a middle point adjustment for the boundaries of confidence intervals. Second, we propose an interpolation approach for evaluating the likelihood ratio profile at non-observable threshold values. Our extensive Monte Carlo simulations suggest that our proposed confidence intervals outperform existing methods, including bootstrap approaches, by attaining very accurate coverage rates with relatively short lengths in finite samples.