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Inference About the Point of Change in a Regression Model
Author(s) -
Esterby S. R.,
ElShaarawi A. H.
Publication year - 1981
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346352
Subject(s) - inference , econometrics , regression analysis , regression , statistics , computer science , artificial intelligence , mathematics
S ummary Consider a sequence of ( n 1 + n 2 ) 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 n 1 . The relative marginal likelihood function for n 1 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.

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