Estimating the Parental Magma Composition and Temperature of the Xiaohaizi Cumulate-Bearing Ultramafic Rock: Implication for Magma Evolution of the Tarim Large Igneous Province, Northwestern China

The ultramafic dikes in the Tarim large igneous province（Tarim LIP）, exposed in the Xiaohaizi area in the northwestern Tarim Basin of northwestern China, have porphyritic textures, and the olivine and clinopyroxene are as the major phenocryst phases. The groundmass therein consists of clinopyroxene, plagioclase and Fe-Ti oxides, with the cryptocrystalline texture. The olivine phenocrysts in one typical ultramafic dike have Fo（Mg/（Mg＋Fe）） numbers ranging from 73 to 85, which are not in equilibrium with the olivine（Mg# of 89） from the host rock crystalized. Combined with microscope observation, both the olivine and clinopyroxene phenocrysts as well as some Fe-Ti oxides in the ultramafic rock are accounted as cumulates. The liquid（parental magma） composition of SiO2 of 45.00 wt.%–48.82 wt.%, MgO of 9.93 wt.%– 18.56 wt.%, FeO of 5.85 wt.%–14.17 wt.%, CaO of 7.54 wt.%–11.52 wt.%, Al2O3 of 8.70 wt.%–11.62 wt.% and TiO2 of 0.00 wt.%–3.43 wt.% in the Xiaohaizi ultramafic rock was estimated by mass balance, and the results show a reasonable liquid proportion in the cumulate-bearing ultramafic dike（ca. 45%–60% in the whole rock）. The estimated parental magma composition corresponds to a melting temperature of 1 300–1 550 oC, which is equal or higher than those of a normal asthenosphere mantle, supporting the involvement of a mantle plume. Combined with other previous studies, an evolution model for the formation processes of the Xiaohaizi ultramafic dike of the Tarim LIP is proposed.

Composite Quantile Estimation for Kink Model with Longitudinal Data

Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.

Optimal AK composite estimators in current population survey

The Current Population Survey(CPS)is a monthly household sample survey with a sample consisting of eight rotation groups.Sampled individuals of a rotation group are interviewed four consecutive months and another four consecutive months after resting eight consecutive months.A composite-type estimator is adopted in the CPS for the estimation of the monthly population total,which combines sample information from the current month’s survey and previous months using the fact that 75%households have data for two consecutive months.There are two values,A and K,in the composite estimator to decide how to combine the available information,and thus this estimator is called the AK composite estimator.In this paper,we use a formula of the meansquared error of AK composite estimator and propose an easy-to-use method of choosing A and K based on data,which evolves the estimation of some population quantities using the method of moments and replication.Some numerical studies are conducted to illustrate the effectiveness of the proposed method.