Estimation of parameters in the joinpoint two-regime regression model

Of interest is the specific model called the joinpoint two-regime regression or broken line model composed of one regression line and a horizontal ray. This is a very restricted but highly useful subset of the well-researched change point problem. The usual approach, first presented by Quandt (1958), is to find estimates of the slope, intercept, and joinpoint by assuming that the error terms are generated from a normal distribution. For our specific model this method of estimation was shown by Gill (2004) to produce the maximum likelihood estimates. We develop a method that does not rely on the assumption of normal, independent, identically distributed (iid) error terms. We illustrate the method by applying it to proximity indexes of whale cow and calf pairs, and compare our new method to the Quandt estimates in a simulation study showing our new method performs adequately in the normal iid error term model and is preferable in small samples where error terms are correlated with non constant variance.