A Partially Linear Framework for Massive Heterogeneous Data

We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (non-asymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. This oracular result holds when the number of sub-populations does not grow too fast. A plug-in estimator for the heterogeneity parameter is further constructed, and shown to possess the asymptotic distribution as if the commonality information were available. We also test the heterogeneity among a large number of sub-populations. All the above results require to regularize each sub-estimation as though it had the entire sample size. Our general theory applies to the divide-and-conquer approach that is often used to deal with massive homogeneous data. A technical by-product of this paper is the statistical inferences for the general kernel ridge regression. Thorough numerical results are also provided to back up our theory.Comment: 40 pages main text + 40 pages suppl, To appear in Annals of Statistic

Self-desiccation and self-desiccation shrinkage of silica fume-cement pastes

Self-desiccation is one common phenomenon of high-performance cementitious materials, which are characterized by low water/binder (w/b) ratio and high mineral admixture incorporation. As a consequence, large magnitude of self-desiccation shrinkage, a key factor which influences the cracking behavior of concrete, develops rapidly in the cement matrix due to the internal relative humidity (RH) decrease and capillary pressure induced by self-desiccation. The objective of this study is to evaluate the behavior of self-desiccation and self-desiccation shrinkage in silica fume (SF) blended cement pasts with low w/b ratio of 0.25. The self-desiccation process was revealed by the measurement of internal RH of the sealed cement pastes with conventional method of hygrometer. The shrinkage of the sealed cement pastes was measured by the corrugated tube method, permitting measurements to start at early age. Experimental results revealed that SF blending leads to a higher internal RH, indicating slower self-desiccation process, compared with pure cement paste. Consequently, less self-desiccation shrinkage was observed in SF blended cement pastes than that in pure cement paste