• 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.

• The Journal of the Petrological Society of Korea
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• v.11 no.3_4
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• pp.200-213
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• 2002

The Andong granitoid batholith represents five temporally distinct episodes (phases) of igneous activity. The batholith represents a plutonic complex of five pulsatively emplaced distinct intrusive multiphases. The petrochemical data show that the plutons fall into calc-alkaline series except for the Yean pluton, and plot within the diaenostic range for I-type origin and continental arc orogenic tectonic setting. Each pluton reveals systematic compositional variations of major and trace elements with $SiO_2$ or MgO, but different variation trends for some elements and considerably different REE patterns. Thus discontinuous, inconsistent variations in the elements indicate that the five plutons can not be explained by simple fractional crystallization from the same primary magma, but were intruded and solidified from the independent magmas of chemically heterogeneous origin. In the Andong, Dosan and Pungsan plutons, high values of molar CaO/(MgO+$FeO^{t}$ ) combined with low $Al_2$$O_3$/(MgO+$FeO^{t}$ ) and $K_2$O$Na_2$O ratios suggest a magma originated by dehydration melting of a metabasaltic to metatonalitic protolith. Whereas the Imha pluton show similar values of CaO/(MgO+$FeO^{t}$ ), but significantly higher ratios of $Al_2$$O_3$/(MgO+$FeO^{t}$ ) and $K_2$O$Na_2$O implying to a metagreywacke protolith.