RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-free knockoffs procedure introduced recently in Cand\`{e}s, Fan, Janson and Lv (2016) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.Comment: 37 pages, 6 tables, 9 pages supplementary materia

Robust rank correlation based screening

Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as large as an exponential of the sample size n. In this paper we propose a robust rank correlation screening (RRCS) method to deal with ultra-high dimensional data. The new procedure is based on the Kendall \tau correlation coefficient between response and predictor variables rather than the Pearson correlation of existing methods. The new method has four desirable features compared with existing independence screening methods. First, the sure independence screening property can hold only under the existence of a second order moment of predictor variables, rather than exponential tails or alikeness, even when the number of predictor variables grows as fast as exponentially of the sample size. Second, it can be used to deal with semiparametric models such as transformation regression models and single-index models under monotonic constraint to the link function without involving nonparametric estimation even when there are nonparametric functions in the models. Third, the procedure can be largely used against outliers and influence points in the observations. Last, the use of indicator functions in rank correlation screening greatly simplifies the theoretical derivation due to the boundedness of the resulting statistics, compared with previous studies on variable screening. Simulations are carried out for comparisons with existing methods and a real data example is analyzed.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1024 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:0903.525

Silica nanospheres entrapped with ultra-small luminescent crystals for protein delivery

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Constructing smart nano-systems for intracellular delivery of functional proteins has been endeavored for diverse biomedical applications, but suffered daunting challenges. Herein silica nanospheres entrapped with photoluminescent CaF2:Tm,Yb nanocrystals were synthesized and decorated with amino molecules for protein delivery. Amino-modified nanospheres presented high protein loading capacity and sustained release phenomenon. The photoluminescence of particles highly corresponded to protein release progress. The preliminary in-vitro study confirmed markedly enhanced cell up-taking efficiency of protein molecules with the nanocomposite developed

Room-temperature nonequilibrium growth of controllable ZnO nanorod arrays

In this study, controllable ZnO nanorod arrays were successfully synthesized on Si substrate at room temperature (approx. 25°C). The formation of controllable ZnO nanorod arrays has been investigated using growth media with different concentrations and molar ratios of Zn(NO3)2 to NaOH. Under such a nonequilibrium growth condition, the density and dimension of ZnO nanorod arrays were successfully adjusted through controlling the supersaturation degree, i.e., volume of growth medium. It was found that the wettability and electrowetting behaviors of ZnO nanorod arrays could be tuned through variations of nanorods density and length. Moreover, its field emission property was also optimized by changing the nanorods density and dimension

Enhanced Luminescence of Eu-Doped TiO2Nanodots

Monodisperse and spherical Eu-doped TiO2nanodots were prepared on substrate by phase-separation-induced self-assembly. The average diameters of the nanodots can be 50 and 70 nm by changing the preparation condition. The calcined nanodots consist of an amorphous TiO2matrix with Eu3+ions highly dispersed in it. The Eu-doped TiO2nanodots exhibit intense luminescence due to effective energy transfer from amorphous TiO2matrix to Eu3+ions. The luminescence intensity is about 12.5 times of that of Eu-doped TiO2film and the luminescence lifetime can be as long as 960 μs