### Abstract

Language | English |
---|---|

Journal | Statistica Sinica |

Status | Published - 2013 |

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*Statistica Sinica*.

**Dependent functional linear models with applications to monitoring structural change.** / Aue, A.; Hörmann, Siegfried; Horvath, Lajos; Huskovà, M.

Research output: Contribution to journal › Article › Research › peer-review

*Statistica Sinica*.

}

TY - JOUR

T1 - Dependent functional linear models with applications to monitoring structural change

AU - Aue, A.

AU - Hörmann, Siegfried

AU - Horvath, Lajos

AU - Huskovà, M.

N1 - DOI: 10.5705/ss.2012.233

PY - 2013

Y1 - 2013

N2 - We study sequential monitoring procedures that detect instabilities of the regression operator in an underlying (fully) functional regression model allowing for dependence. These open-end and closed-end procedures are built on a functional principal components analysis of both the predictor and response functions, thus giving rise to multivariate detector functions, whose fluctuations are compared against a curved threshold function. The main theoretical result of the paper quantifies the large-sample behavior of the procedures under the null hypothesis of a stable regression operator. To establish these limit results, classical results on functional principal components analysis are generalized to a dependent setting, which may be of interest in its own sake. In an accompanying empirical study we illustrate the finite sample properties, while an application to environmental data highlights practical usefulness. To the best of our knowledge this is the first paper that combines sequential with functional data methodology.

AB - We study sequential monitoring procedures that detect instabilities of the regression operator in an underlying (fully) functional regression model allowing for dependence. These open-end and closed-end procedures are built on a functional principal components analysis of both the predictor and response functions, thus giving rise to multivariate detector functions, whose fluctuations are compared against a curved threshold function. The main theoretical result of the paper quantifies the large-sample behavior of the procedures under the null hypothesis of a stable regression operator. To establish these limit results, classical results on functional principal components analysis are generalized to a dependent setting, which may be of interest in its own sake. In an accompanying empirical study we illustrate the finite sample properties, while an application to environmental data highlights practical usefulness. To the best of our knowledge this is the first paper that combines sequential with functional data methodology.

M3 - Article

JO - Statistica Sinica

T2 - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

ER -