Multikink quantile regression for longitudinal data with application to progesterone data analysis.

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly.

CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.

Robust Multicategory Support Matrix Machines.

We consider the classification problem when the input features are represented as matrices rather than vectors. To preserve the intrinsic structures for classification, a successful method is the Support Matrix Machine (SMM) in [19], which optimizes an objective function with a hinge loss plus a so-called spectral elastic net penalty. However, the issues of extending SMM to multicategory classification still remain. Moreover, in practice, it is common to see the training data contaminated by outlying observations, which can affect the robustness of existing matrix classification methods. In this paper, we address these issues by introducing a robust angle-based classifier, which boils down binary and multicategory problems to a unified framework. Benefitting from the use of truncated hinge loss functions, the proposed classifier achieves certain robustness to outliers. The underlying optimization model becomes nonconvex, but admits a natural DC (difference of two convex functions) representation. We develop a new and efficient algorithm by incorporating the DC algorithm and primal-dual first-order methods together. The proposed DC algorithm adaptively chooses the accuracy of the subproblem at each iteration while guaranteeing the overall convergence of the algorithm. The use of primal-dual methods removes a natural complexity of the linear operator in the subproblems and enables us to use the proximal operator of the objective functions, and matrix-vector operations. This advantage allows us to solve large-scale problems efficiently. Theoretical and numerical results indicate that for problems with potential outliers, our method can be highly competitive among existing methods.

Is the wash-off process of road-deposited sediment source limited or transport limited?

An in-depth understanding of the road-deposited sediments (RDS) wash-off process is essential to estimation of urban surface runoff pollution load and to designing methods to minimize the adverse impacts on the receiving waters. There are two debatable RDS wash-off views: source limited and transport limited. The RDS build-up and wash-off process was characterized to explore what determines the wash-off process to be source limited or transport limited based on twelve RDS sampling activities on an urban road in Beijing. The results showed that two natural rain events (2.0mm and 23.2mm) reduced the total RDS mass by 30%-40%, and that finer particles (<105µm) contributed 60%-80% of the wash-off load. Both single- and multi-rain events caused the RDS particle grain size to become coarser, while dry days made the RDS particle grain size finer. These findings indicated that the bulk RDS particles wash-off tends to be transport limited, but that finer particles tend to be source limited. To further explore and confirm the results of the field experiment, a total of 40 simulated rain events were designed to observe the RDS wash-off with different particle size fractions. The finer particles have a higher wash-off percentage (Fw) than the coarser particles, and the Fw values provide a good view to characterize the wash-off process. The key conclusions drawn from the combined field and simulated experiments data are: (i) Finer and coarser particle wash-off processes tend to be source limited and transport limited, respectively. (ii) The source and transport limited processes occur during the initial period (the first flush) and later periods, respectively. (iii) The smaller and larger rain events tend to be transport limited and source limited, respectively. Overall, the wash-off process is generally a combination of source and transport limited processes.

Spatial-Temporal Changes of Bacterioplankton Community along an Exhorheic River.

To date, few aquatic microbial ecology studies have discussed the variability of the microbial community in exorheic river ecosystems on both the spatial and seasonal scales. In this study, we examined the spatio-temporal variation of bacterioplankton community composition in an anthropogenically influenced exorheic river, the Haihe River in Tianjin, China, using pyrosequencing analysis of 16S rRNA genes. It was verified by one-way ANOVA that the spatial variability of the bacterioplankton community composition over the whole river was stronger than the seasonal variation. Salinity was a major factor leading to spatial differentiation of the microbial community structure into riverine and estuarial parts. A high temperature influence on the seasonal bacterial community variation was only apparent within certain kinds of environments (e.g., the riverine part). Bacterial community richness and diversity both exhibited significant spatial changes, and their seasonal variations were completely different in the two environments studied here. Furthermore, riverine bacterial community assemblages were subdivided into urban and rural groups due to changes in the nutritional state of the river. In addition, the nutrient-loving group including Limnohabitans, Hydrogenophaga, and Polynucleobacter were abundant in the urbanized Haihe River, indicating the environmental factors in these anthropogenic waterbodies heavily influence the core freshwater community composition.