Inference About the Point of Change in a Regression Model

S. R. Esterby and A. H. El‐Shaarawi

Journal of the Royal Statistical Society Series C, 1981, vol. 30, issue 3, 277-285

Abstract: Consider a sequence of (n1 + n2) independent ordered pairs of observations for which the relationship between variables can be represented by a segmented polynomial regression model with unknown point of change n1. The relative marginal likelihood function for n1 is derived and the expressions for the relative conditional and maximum likelihood functions are given. Either of the first two likelihoods, which account for the uncertainty about the value of the other parameters, are to be preferred to the maximum likelihood function, with the relative marginal likelihood function being examined more extensively here. In the case where the segmented regression model can be represented by two polynomials of unknown degrees p and q, a procedure is described for estimating p and q. The use of these methods is illustrated using two observed sets of data and three artificially generated sets.

Date: 1981
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