Asymptotics and confidence estimation in segmented regression models.

Abstract

ASYMPTOTICS AND CONFIDENCE ESTIMATION IN SEGMENTED REGRESSION MODELS Rebekah Ann Robinson May 11, 2012 Standard regularity assumptions for regression models are not satisfied in segmented regression models with an unknown change point, and consequently standard asymptotic results and inferential methods for confidence estimation are not applicable. This dissertation considers a clustered segmented regression model with a continuity constraint and considers estimators of the model parameters based on the likelihood principle. The strong consistency of the maximum likelihood estimators is established. To consider the asymptotic distribution, two cases must be considered. Case 1 occurs when the true change point occurs between two of the observation times, while Case 2 occurs when the true change point occurs at one of the observation times. In each case, the asymptotic distribution of relevant estimators is derived. These results are used to develop a new comprehensive algorithm for constructing a confidence interval for the change point parameter which works for both cases using all available data in determining the confidence bounds. This algorithm is compared to an existing method known as the removal algorithm. A slight modification to the comprehensive algorithm is also considered. Finally, these methods for obtaining confidence intervals are compared by simulation studies and applied to a real data set.