Classical regression methods have focused mainly on estimating conditional mean functions. In recent years, however, quantile regression has emerged as a comprehensive approach to the statistical analysis of response models. In this article we consider the L 1 -norm (LASSO) regularized quantile regression (L 1 -norm QR), which uses the sum of the absolute values of the coefficients as the penalty. The L 1 -norm penalty has the advantage of simultaneously controlling the variance of the fitted coefficients and performing automatic variable selection. We propose an efficient algorithm that computes the entire solution path of the L 1 -norm QR. Furthermore, we derive an estimate for the effective dimension of the L 1 -norm QR model, which allows convenient selection of the regularization parameter.

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The Qilian Shan, at the northeastern frontier of the Tibetan Plateau, is a key area for studying the expansion mechanism of the Tibetan Plateau. Although previous thermochronology and paleomagnetic studies indicate Neogene northward expansion of the northern Qilian Shan, there is a distinct temporal gap in knowledge relative to the tectonic history of the southern Qilian Shan. This has hindered a complete understanding of the Cenozoic deformation pattern of the entire Qilian Shan. To study the growth history of the southern Qilian Shan, apatite fission track (AFT) data have been acquired from Zongwulong Shan and the Huaitoutala section. AFT thermal history modeling from the former shows a rapid cooling episode occurred at~18-11 Ma, which is interpreted as marking the onset of intensive exhumation in the southern Qilian Shan. Within the Huaitoutala section, detrital grain up-section shows progressively decreasing peak AFT ages followed by an age increase from midsection, implying that a sediment-recycling event occurred at approximately 7 ± 2 Ma. Together with a shift in paleocurrent directions, this change marks the onset of Late Miocene deformation of the northern Qaidam Basin. Combined with previous studies on the deformation time of the Qilian Shan, our findings suggest that both the northern and southern Qilian Shan region grew outward synchronously in opposite directions during the Neogene. This resulted in the formation of a flower structure, which had an important impact on the deformation pattern of north Tibet. The synchronous outward expansion may have been triggered by the removal of mantle beneath north Tibet.

The northern Tibetan Plateau, north of the Qaidam Basin and south of the Hexi Corridor (China), consists of a series of WNW-to NW-trending elongated mountain ranges. Deciphering the time-space deformation pattern of these ranges is central to understanding the mechanism of plateau formation and to the controversial issue of whether Tibet has undergone progressive northward growth or synchronous growth since the India-Eurasia collision. Here, we report new constraints on the timing of accelerated uplift of the Tuolai Shan, one of the elongated mountain ranges in the northern Tibetan Plateau. New apatite fission-track data from an elevation transect in the Tuolai Shan provide a definitive tie to rapid cooling that began at 17-15 Ma. We attribute this rapid cooling to accelerated exhumation resulting from thrusting in the hanging wall of the Haiyuan fault in response to progressive northward growth of the plateau. Combining these fission-track data and the published geologic, sedimentological, and thermochronologic data from the northern Qilian Shan and Hexi Corridor, we propose a progressively north-northeastward growth model for the northernmost part of Tibet, suggesting that deformation in the inner Qilian Shan occurred synchronously in the middle Miocene, and subsequently, increasingly further north.