A common approach to detect multiple changepoints is to minimise a measure of data fit plus a penalty that is linear in the number of changepoints. This paper shows that the general finite sample behaviour of such a method can be related to its behaviour when analysing data with either none or one changepoint. This results in simpler conditions for verifying whether the method will consistently estimate the number and locations of the changepoints. We apply and demonstrate the usefulness of this result for a range of changepoint problems. Our new results include a weaker condition on the choice of penalty required to have consistency in a change-in-slope model; and the first results for the accuracy of recently-proposed methods for detecting spikes.
翻译:一种常见的检测多变点的方法是将适合的数据量与修改点数的线性惩罚最小化。本文表明,在分析数据时,这种方法的一般有限抽样行为可能与它的行为有关,而分析数据时没有或只有一个修改点。这为核实该方法是否将一致估计修改点的数量和位置提供了更简单的条件。我们应用这一结果,并证明它对于一系列修改点问题有用。我们的新结果包括:在选择刑罚方面条件较弱,而选择刑罚是为了在改变式模型中保持一致;以及最近提出的检测激增方法的最初准确性结果。