This paper deals with the asymptotic distribution theory of least squares estimators in regression models having different analytical forms in different regions of the domain of the independent variable. An important special case is that of broken line regression, in which each segment of the regression function is a different straight line. The residual sum of squares function has many corners, and so classical least squares techniques cannot be directly applied. It is shown, however, that the problem can be transformed into a new problem in which the sum of squares function is locally smooth enough to apply the classical techniques. Asymptotic distribution theory is discussed for the new problem and it is shown that the results are also valid for the original problem. Results related to the usual normal theory are derived.
"On Asymptotic Distribution Theory in Segmented Regression Problems-- Identified Case." Ann. Statist. 3 (1) 49 - 83, January, 1975. https://doi.org/10.1214/aos/1176342999