Asymptotic results in segmented multiple regression

Jeankyung Kim and Hyune-Ju Kim

Journal of Multivariate Analysis, 2008, vol. 99, issue 9, 2016-2038

Abstract: This paper studies the asymptotic behavior of the least squares estimators in segmented multiple regression. For a model with more than one partitioning variable, each of which has one or more change-points, we study the asymptotic properties of the estimated change-points and regression coefficients. Using techniques in empirical process theory, we prove the consistency of the least squares estimators and also establish the asymptotic normality of the estimated regression coefficients. For the estimated change-points, we obtain their consistency at the rates of or 1/n, with or without continuity constraints, respectively. The change-points estimated under the continuity constraints are also shown to asymptotically have a multivariate normal distribution. For the case where the regression mean functions are not assumed to be continuous at the change-points, the asymptotic distribution of the estimated change-points involves a step function process, whose distribution does not follow a well-known distribution.

Keywords: primary; 62J02 secondary; 62E20 Empirical process Change-point Consistency Asymptotic normality (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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