On the calculations of the maximum likelihood estimates for the polynomial spline regression model with unknown knots and ar(1) errors

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Abstract

Asymptotic distributions of the maximum likelihood estimators of the regression coefficients and knot points for the polynomial spline regression models with unknown knots and AR(1) errors have been derived by Chan (1989). Chan showed that under some mild conditions the maximum likelihood estimators, after suitable standardization, asymptotically follow normal distributions as n diverges to infinity. For the calculations of the maximum likelihood estimators, iterative methods must be applied. But this is not easy to implement for the model considered. In this paper, we suggested an alternative method to compute the estimates of the regression parameters and knots. It is shown that the estimates obtained by this method are asymptotically equivalent to the maximum likelihood estimates considered by Chan.

Original languageEnglish
Pages (from-to)1199-1209
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Volume20
Issue number4
DOIs
Publication statusPublished - 1991 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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