Asymptotic results in segmented multiple regression

Jeankyung Kim, Hyune Ju Kim

Research output: Contribution to journalArticle

12 Scopus citations

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 1 / sqrt(n) 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.

Original languageEnglish (US)
Pages (from-to)2016-2038
Number of pages23
JournalJournal of Multivariate Analysis
Volume99
Issue number9
DOIs
StatePublished - Oct 2008

Keywords

  • 62E20
  • 62J02
  • Asymptotic normality
  • Change-point
  • Consistency
  • Empirical process
  • primary
  • secondary

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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