• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.863-874
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• 2021

In this paper, we propose a post-selection inference procedure for the fused lasso signal approximator (FLSA). The FLSA finds underlying sparse piecewise constant mean structure by applying total variation (TV) semi-norm as a penalty term. However, it is widely known that this convex relaxation can cause asymptotic inconsistency in change points detection. As a result, there can remain false change points even though we try to find the best subset of change points via a tuning procedure. To remove these false change points, we propose a post-selection inference for the FLSA. The proposed procedure applies a permutation test based on CUSUM statistic. Our post-selection inference procedure is an extension of the permutation test of Antoch and Hušková (2001) which deals with single change point problems, to multiple change points detection problems in combination with the FLSA. Numerical study results show that the proposed procedure is better than naïve z-tests and tests based on the limiting distribution of CUSUM statistics.

• The Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.371-384
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• 2022

The fused LASSO signal approximator (FLSA) can be applied to find change points from the data having piecewise constant mean structure. It is well-known that the FLSA is inconsistent in change points detection. This inconsistency is due to a total-variation denoising penalty of the FLSA. ℓ₁ trend filter, one of the popular tools for finding an underlying trend from data, can be used to identify change points of piecewise linear trends. Since the ℓ₁ trend filter applies the sum of absolute values of slope differences, it can be inconsistent for change points recovery as the FLSA. However, there are few studies on the inconsistency of the ℓ₁ trend filtering. In this paper, we demonstrate the inconsistency of the ℓ₁ trend filtering with a numerical study.