Change-point detection in a linear model by adaptive fused quantile method
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A novel approach to quantile estimation in multivariate linear regression models with change-points is proposed. The change-point detection and the model estimation are both performed automatically, by adopting either the quantile fused penalty or the adaptive version of the quantile fused penalty. These two methods combine the idea of the check function used for the quantile estimation and the L_1 penalization principle known from the signal processing and, unlike some standard approaches, the presented methods go beyond typical assumptions usually required for the model errors, such as sub-Gaussian or Normal distribution. They can effectively handle heavy-tailed random error distributions, and, in general, they offer a more complex view on the data as one can obtain any conditional quantile of the target distribution, not just the conditional mean. Theoretical results are proved and proper convergence rates are derived. The empirical performance is investigated via an extensive comparative simulation study.
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