Nonlinear power function model changepoint detection.

Most work surrounding changepoint analysis focuses on linear models. This dissertation explores changepoint detection in nonlinear power function models, specifically focusing on models where the constant multiplier and power are the parameters to be estimated in addition to the changepoint parameter. The study assumes an asymptotic framework as the number of observations approaches infinity. The study explores various model fitting algorithms, and decides to employ the Newton-Raphson method for parameter estimation, with a custom implementation developed to optimize the process. The research first establishes the strong consistency of estimators for the model without a changepoint. Building on this result, consistency is then demonstrated for the model incorporating a changepoint. Asymptotic normality is then explored for the model parameters other than the changepoint. The dissertation develops a novel matrix-based formulation of the error function, enabling a simplified analysis of the model’s properties. Detailed derivations of the first and second derivatives of the error function are presented, along with an exploration of the rank and invertibility of the second derivative matrix.