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Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression with large-scale data in the "increasing dimension" regime. We provide a comprehensive and in-depth analysis of a convolution-type smoothing approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as {\it{conquer}}, turns the non-differentiable quantile loss function into a twice-differentiable, convex and locally strongly convex surrogate, which admits a fast and scalable Barzilai-Borwein gradient-based algorithm to perform optimization, and multiplier bootstrap for statistical inference. Theoretically, we establish explicit non-asymptotic bounds on both estimation and Bahadur-Kiefer linearization errors, from which we show that the asymptotic normality of the conquer estimator holds under a weaker requirement on the number of the regressors than needed for conventional quantile regression. Moreover, we prove the validity of multiplier bootstrap confidence constructions. Our numerical studies confirm the conquer estimator as a practical and reliable approach to large-scale inference for quantile regression. Software implementing the methodology is available in the \texttt{R} package \texttt{conquer}., An R package conquer for fitting smoothed quantile regression is available in CRAN, https://cran.r-project.org/web/packages/conquer/index.html

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting statistical inference. Principal component analysis, commonly referred to as PCA, has become an essential tool for multivariate data analysis and unsupervised dimension reduction, the goal of which is to find a lower dimensional subspace that captures most of the variation in the dataset. This article provides an overview of methodological and theoretical developments of PCA over the last decade, with focus on its applications to big data analytics. We first review the mathematical formulation of PCA and its theoretical development from the view point of perturbation analysis. We then briefly discuss the relationship between PCA and factor analysis as well as its applications to large covariance estimation and multiple testing. PCA also finds important applications in many modern machine learning problems, and we focus on community detection, ranking, mixture model and manifold learning in this paper., review article, in press with Wiley StatsRef

Anti-Mullerian hormone (AMH) acts in maintaining orderly cyclic recruitment of early follicles, suggesting that it is a promising candidate for influencing animal reproductive efficiency. This study aimed to elucidate the effect of a missense mutation of Val566Ile on the structure of AMH protein and the genetic association of Val566Ile and AMH expression with egg production in chickens. Structural perturbations of Val566Ile were predicted by homology modeling. The association of the variant with the number of eggs was tested using a quantitative trait transmission disequilibrium test model. AMH expression in granulosa cells in Lueyang black-boned chickens was compared with that in Nick chickens. The Val566 of AMH is a non-conservative amino acid among mammals and birds, but its hydrophobicity is completely conservative. The substitution of Val566 for Ile566 potentially disrupted hydrogen bonds and solvent accessibility of 22 residues and created a short α-helix in the C terminus of AMH. Despite having striking structure-disrupting potential, the variant was not statistically associated with the number of eggs (P>0.05) in the Lueyang black-boned chickens. We did not detect differential expression of AMH between Lueyang black-boned chickens and Nick chickens (P>0.05). These results confirmed the structural impact of Val566Ile, but suggested that Val566Ile and AMH expression might not be the major genetic determinants for egg production in Lueyang black-boned chickens.

Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified analysis of the smoothed sequential estimator and its penalized counterpart in increasing dimensions. When the covariate dimension grows with the sample size at a sublinear rate, we establish the uniform convergence rate (over a range of quantile indexes) and provide a rigorous justification for the validity of a multiplier bootstrap procedure for inference. In high-dimensional sparse settings, our results considerably improve the existing work on CQR by relaxing an exponential term of sparsity. We also demonstrate the advantage of the smoothed CQR over existing methods with both simulated experiments and data applications.

This paper establishes non-asymptotic concentration bound and Bahadur representation for the quantile regression estimator and its multiplier bootstrap counterpart in the random design setting. The non-asymptotic analysis keeps track of the impact of the parameter dimension $d$ and sample size $n$ in the rate of convergence, as well as in normal and bootstrap approximation errors. These results represent a useful complement to the asymptotic results under fixed design and provide theoretical guarantees for the validity of Rademacher multiplier bootstrap in the problems of confidence construction and goodness-of-fit testing. Numerical studies lend strong support to our theory and highlight the effectiveness of Rademacher bootstrap in terms of accuracy, reliability and computational efficiency.

The robustification parameter, which balances bias and robustness, has played a critical role in the construction of sub-Gaussian estimators for heavy-tailed and/or skewed data. Although it can be tuned by cross-validation in traditional practice, in large scale statistical problems such as high dimensional covariance matrix estimation and large scale multiple testing, the number of robustification parameters scales with the dimensionality so that cross-validation can be computationally prohibitive. In this paper, we propose a new data-driven principle to choose the robustification parameter for Huber-type sub-Gaussian estimators in three fundamental problems: mean estimation, linear regression, and sparse regression in high dimensions. Our proposal is guided by the non-asymptotic deviation analysis, and is conceptually different from cross-validation which relies on the mean squared error to assess the fit. Extensive numerical experiments and real data analysis further illustrate the efficacy of the proposed methods

$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave regularization may lead to estimators with refined convergence rates and oracle properties as the signal strengthens. Although folded concave penalized $M$-estimation with strongly convex loss functions have been well studied, the extant literature on quantile regression is relatively silent. The main difficulty is that the quantile loss is piecewise linear: it is non-smooth and has curvature concentrated at a single point. To overcome the lack of smoothness and strong convexity, we propose and study a convolution-type smoothed quantile regression with iteratively reweighted $\ell_1$-regularization. The resulting smoothed empirical loss is twice continuously differentiable and (provably) locally strongly convex with high probability. We show that the iteratively reweighted $\ell_1$-penalized smoothed quantile regression estimator, after a few iterations, achieves the optimal rate of convergence, and moreover, the oracle rate and the strong oracle property under an almost necessary and sufficient minimum signal strength condition. Extensive numerical studies corroborate our theoretical results., Comment: Main text is 27 pages, online supplementary materials are attached after the main text

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moments, we show that iteratively reweighted l1-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as O(logs+loglogd) iterations to reach such an oracle estimator, where s and d denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory.

Distributed data naturally arise in scenarios involving multiple sources of observations, each stored at a different location. Directly pooling all the data together is often prohibited due to limited bandwidth and storage, or due to privacy protocols. This paper introduces a new robust distributed algorithm for fitting linear regressions when data are subject to heavy-tailed and/or asymmetric errors with finite second moments. The algorithm only communicates gradient information at each iteration and therefore is communication-efficient. Statistically, the resulting estimator achieves the centralized nonasymptotic error bound as if all the data were pooled together and came from a distribution with sub-Gaussian tails. Under a finite $(2+\delta)$-th moment condition, we derive a Berry-Esseen bound for the distributed estimator, based on which we construct robust confidence intervals. Numerical studies further confirm that compared with extant distributed methods, the proposed methods achieve near-optimal accuracy with low variability and better coverage with tighter confidence width., Comment: 29 pages

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this paper we propose a Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for large-scale simultaneous inference with control of the false discovery proportion. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is of independent interest, we establish an exponential-type deviation inequality for a robust $U$-type covariance estimator under the spectral norm. Extensive numerical experiments demonstrate the advantage of the proposed method over several state-of-the-art methods especially when the data are generated from heavy-tailed distributions. The proposed procedures are implemented in the R-package FarmTest., Comment: 52 pages, 9 figures

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression, integrated with the multiplier bootstrap procedure, provides a useful robust alternative to the method of least squares. Our theoretical and empirical results reveal the effectiveness of the proposed method, and highlight the importance of having inference methods that are robust to heavy tailedness., Comment: 81 pages, 1 figure

In this work, we study a right time for an investor to stop the investment among multi-assets over a given investment horizon so as to obtain maximum profit. We formulate it to a two-stage problem. The main problem is not a standard optimal stopping problem due to the non-adapted term in the objective function, and we turn it to a standard one by stochastic analysis. The subproblem with control variable in the drift and volatility terms is solved first via stochastic control method. A numerical example is presented to illustrate the efficiency of the theoretical results.

A mild and simple synthesis process for large-scale vanadium redox flow batteries (VRFBs) energy storage systems is desirable. A graphite felt/MnO2 (GF-MNO) composite electrode with excellent electrocatalytic activity towards VO2+/VO2+ redox couples in a VRFB was synthesized by a one-step hydrothermal process. The resulting GF-MNO electrodes possess improved electrochemical kinetic reversibility of the vanadium redox reactions compared to pristine GF electrodes, and the corresponding energy efficiency and discharge capacity at 150 mA cm − 2 are increased by 12.5% and 40%, respectively. The discharge capacity is maintained at 4.8 A h L − 1 at the ultrahigh current density of 250 mA cm − 2. Above all, 80% of the energy efficiency of the GF-MNO composite electrodes is retained after 120 charge-discharge cycles at 150 mA cm − 2. Furthermore, these electrodes demonstrated that more evenly distributed catalytic active sites were obtained from the MnO2 particles under acidic conditions. The proposed synthetic route is facile, and the raw materials are low cost and environmentally friendly. Therefore, these novel GF-MNO electrodes hold great promise in large-scale vanadium redox flow battery energy storage systems.

The development of a three-dimensionally flexible, large-surface area, high-conductivity electrode is important to improve the low conductivity and utilization of active materials and restrict the shuttle of long-chain polysulfides in Li–polysulfide batteries. Herein, we constructed an integrated three-dimensional carbon nanotube forest/carbon cloth electrode with heteroatom doping and high electrical conductivity. The as-constructed electrode provides strong trapping on the polysulfide species and fast charge transfer. Therefore, the Li–polysulfide batteries with as-constructed electrodes achieved high specific capacities of ∼1200 and ∼800 mA h g–1 at 0.1 and 1 C, respectively. After 300 cycles at 0.5 C, a specific capacity of 623 mA h g–1 was retained.

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods., 56 pages, 2 figures

We investigate the asymptotic behavior of several variants of the scan statistic applied to empirical distributions, which can be applied to detect the presence of an anomalous interval with any length. Of particular interest is Studentized scan statistic that is preferable in practice. The main ingredients in the proof are Kolmogorov's theorem, a Poisson approximation, and recent technical results by Kabluchko et al (2014).

In this paper, a flow frame with multi-distribution channels is designed. The electrolyte flow distribution in the graphite felt electrode is simulated to be uniform at some degree with the tool of a commercial computational fluid dynamics (CFD) package of Star-CCM+. A 5 kW-class vanadium redox flow battery (VRB) stack composed of 40 single cells is assembled. The electrochemical performance of the VRB stack is investigated. Under the applied current density of 60 mA cm−2 during the charge and discharge processes, the current and energy efficiencies are delivered to be 93.9 and 80.8 %, respectively. A higher average output power of 7.2 kW can be achieved at the current density of 80 mA cm−2 with a lower energy efficiency of 78.4 %. The studies of kW-class VRB stack can be beneficial to the development of large-scale energy storage.

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and is available on CRAN.

Stein’s method is a powerful tool for proving central limit theorems along with explicit error bounds in probability theory, where uniform and non-uniform Berry–Esseen bounds spark general interest. Nonlinear statistics, typified by Hoeffding’s class of U -statistics, L -statistics, random sums and functions of nonlinear statistics, are building blocks in various statistical inference problems. However, because the standardized statistics often involve unknown nuisance parameters, the Studentized analogues are most commonly used in practice. This paper begins with a brief review of some standard techniques in Stein’s method, and their applications in deriving Berry–Esseen bounds and Cramer moderate deviations for nonlinear statistics, and then using the concentration inequality approach, establishes Berry–Esseen bounds for Studentized nonlinear statistics in a general framework. As direct applications, sharp Berry–Esseen bounds for Studentized U - and L - statistics are obtained.

With the rapid development of online shopping and traditional physical store shopping interweaving to form different shopping situations, customer experience has gradually become the main source of retailers&rsquo, sustainable competitive advantage through differentiation. Retailers need to continuously improve customer experience in different shopping situations to maintain long-term sustainable customer satisfaction and achieve sustainability. The study aims to examine what kind of shopping situations will influence customer experience and customer satisfaction. A total of 288 questionnaires were collected from two different shopping situations (146 questionnaires from physical stores were collected in five cities in China and 142 online questionnaires were collected from 21 provinces in China), and multiple regression analysis was adopted to test the hypotheses. As a result, we found that customer experience with staff service, shopping environment, and shopping procedure has a positive influence on customer satisfaction. Different shopping situations significantly moderate the relationships among customer experience with the shopping environment, product experience, and customer satisfaction but rarely influence customer experience with staff service and service procedures. Finally, gender significantly moderates the relationship between customer experience and customer satisfaction in different shopping situations. This study theoretically reveals the relationship between customer experience and satisfaction in different shopping situations and provides practical suggestions for retailers to form differentiated sustainable competitive advantage through customer experience management.

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. In this paper, we develop nonasymptotic concentration results for such an adaptive Huber estimator, namely, the Huber estimator with the tuning parameter adapted to sample size, dimension, and the variance of the noise. Specifically, we obtain a sub-Gaussian-type deviation inequality and a nonasymptotic Bahadur representation when noise variables only have finite second moments. The nonasymptotic results further yield two conventional normal approximation results that are of independent interest, the Berry-Esseen inequality and Cram\'er-type moderate deviation. As an important application to large-scale simultaneous inference, we apply these robust normal approximation results to analyze a dependence-adjusted multiple testing procedure for moderately heavy-tailed data. It is shown that the robust dependence-adjusted procedure asymptotically controls the overall false discovery proportion at the nominal level under mild moment conditions. Thorough numerical results on both simulated and real datasets are also provided to back up our theory., Comment: Ann. Statist. (in press)

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [Ann. Statist. 1 (1973) 799–821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. In this paper, we develop nonasymptotic concentration results for such an adaptive Huber estimator, namely, the Huber estimator with the tuning parameter adapted to sample size, dimension, and the variance of the noise. Specifically, we obtain a sub-Gaussian-type deviation inequality and a nonasymptotic Bahadur representation when noise variables only have finite second moments. The nonasymptotic results further yield two conventional normal approximation results that are of independent interest, the Berry-Esseen inequality and Cramér-type moderate deviation. As an important application to large-scale simultaneous inference, we apply these robust normal approximation results to analyze a dependence-adjusted multiple testing procedure for moderately heavy-tailed data. It is shown that the robust dependence-adjusted procedure asymptotically controls the overall false discovery proportion at the nominal level under mild moment conditions. Thorough numerical results on both simulated and real datasets are also provided to back up our theory.

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest., Comment: to appear in Bernoulli

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-uniform and unknown sampling distributions. This method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear-norm penalized approach, and makes low-rank matrix recovery feasible in more practical settings. Theoretically, we prove that the proposed estimator achieves fast rates of convergence under different settings. Computationally, we propose an alternating direction method of multipliers algorithm to efficiently compute the estimator, which bridges a gap between theory and practice of machine learning methods with max-norm regularization. Further, we provide thorough numerical studies to evaluate the proposed method using both simulated and real datasets., 32 pages, 4 figures

The nickel ions in industrial wastewater derive from electroplating and chemical plating industry. Heavy metal ions can result in water pollution, and do harm to people’s health. Maifanite is a kind of nontoxic and harmless silicate rock mineral materials which have a certain biological activity. Maifanite porthole effect and surface effect can apply to removal of heavy metal ions from wastewater, for example, nickel ion, etc. However, natural Maifanite porous structure could be jammed by humus and sediment gradually; in order to play better adsorption performance of Ni (II) and other heavy metal ions in water, we need to adopt necessary modification treatment processes. H2SO4 was used to modify Maifanite, which prepared a high efficient adsorbent. At the same time, the removal effect of Ni (II) in water at different acid concentration, dosage, temperature, time and etc. was studied. The results showed that the Maifanite obtain better adsorption of 90% when the acid concentration was 2.5 mol/L, dosage of 50 mL, contact time and temperature of Ni (II) were 0.5 h and 30°C respectively. The above treatment has certain effect and meaning to reduce harm extent of industrial wastewater on environment and human health.

Many data-mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous possibilities of such selections. How can we know statistically our discoveries better than those by chance? In this paper, we define a measure of goodness of spurious fit, which shows how good a response variable can be fitted by an optimally selected subset of covariates under the null model, and propose a simple and effective LAMM algorithm to compute it. It coincides with the maximum spurious correlation for linear models and can be regarded as a generalized maximum spurious correlation. We derive the asymptotic distribution of such goodness of spurious fit for generalized linear models and L1-regression. Such an asymptotic distribution depends on the sample size, ambient dimension, the number of variables used in the fit, and the covariance information. It can be consistently estimated by multiplier bootstrapping and used as a benchmark to guard against spurious discoveries. It can also be applied to model selection, which considers only candidate models with goodness of fits better than those by spurious fits. The theory and method are convincingly illustrated by simulated examples and an application to the binary outcomes from German Neuroblastoma Trials.

The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student’s t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical problems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robustness property of Studentization/self-normalization against heavy-tailed sampling distributions. This paper gives an overview of the salient progress of self-normalized limit theory, from Student’s t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one- and two-sample U-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence.

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded $(1+\delta)$-th moment for any $\delta > 0$. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when $\delta \geq 1$, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime $0, Comment: final version

This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman's smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components., Comment: 40 pages, 3 figures

A new kind of the electromagnetic shielding composite coatings with high performance was prepared using the Ni-Cu-coated glass fibers and nickel powders as fillers and using epoxy resin as binder. The effects of the fibers on the conductivity and electromagnetic shielding effectiveness of the coatings were studied. The study results show as follows: 1) when the optimum ratio of the fillers to epoxy resin is 4:1, the coatings containing 6 wt% the Ni-Cu-coated glass fibers has best conductivity and electromagnetic shielding effectiveness; when the coating layer thickness is 300 μm, the shielding effectiveness of the coatings is up to 43.71-52.31 dB and increased an average of 13.94 dB compared with the nickel powders/ epoxy resin electromagnetic shielding coatings in the frequency range of 0.3-1000 MHz. This offers a new idea to enhance the added value of the glass fibers and the prevention of electromagnetic environmental pollution.

Electromagnetic radiation pollution and its protection has become one of the hot issues of urban development process. This paper analyzed the cause of natural and man-made electromagnetic environment pollution, pointed out the harm of public health and the city normal production and living order and the city sustainable development. This paper suggested that comprehensive treatment measures should be taken to solve the problem of electromagnetic environment pollution in cities including the reasonable planning and layout, the real powerful supervision, the advertisement and education, and the high level of protection technology. This plays an important role and realistic significance in building a harmonious urban electromagnetic environment.

Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cram\'{e}r-type moderate deviation theorems for Studentized two-sample $U$-statistics in a general framework, including the two-sample $t$-statistic and Studentized Mann-Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample $t$-statistic. These results extend the applicability of the existing statistical methodologies from the one-sample $t$-statistic to more general nonlinear statistics. Applications to two-sample large-scale multiple testing problems with false discovery rate control and the regularized bootstrap method are also discussed., Comment: Published at http://dx.doi.org/10.1214/15-AOS1375 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic datasets and an human acute lymphoblastic leukemia gene expression dataset, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN., Comment: 34 pages, 10 figures; Accepted for biometrics

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the unobserved undistorted data, they have the same first order asymptotic properties as the standard estimators that could be computed if the undistorted data were available. We illustrate the good numerical performance of our methods on both simulated and real datasets., 32 pages, 4 figures

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly when the underlying sampling scheme is non-uniform. In this paper we propose and analyze a max-norm constrained empirical risk minimization method for noisy matrix completion under a general sampling model. The optimal rate of convergence is established under the Frobenius norm loss in the context of approximately low-rank matrix reconstruction. It is shown that the max-norm constrained method is minimax rate-optimal and yields a unified and robust approximate recovery guarantee, with respect to the sampling distributions. The computational effectiveness of this method is also discussed, based on first-order algorithms for solving convex optimizations involving max-norm regularization., 33 pages

Poly (phenylene sulfide) (PPS)/nano-ZnO composites were prepared by DAKA miniature blending instrument. Isothermal crystallization behavior of PPS composites at 245°C, 250°C, 255°C and 260°C were investigated by means of DSC. The crystallization time of PPS composites is shorter than which of neat PPS at the same crystallization temperature. The Avrami equation was used to analyze DSC data. Results showed that neat PPS is homogeneous nucleation at lower crystallization temperature, which is heterogeneous nucleation at higher crystallization temperature contrarily. PPS/nano-ZnO composites are heterogeneous nucleation at various crystallization temperature, nano-ZnO particles play a role of nucleating agent.

Group testing is a technique employed in large screening studies involving infectious disease, where individuals in the study are grouped before being observed. Parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature, in the case where the binary variable indicating the disease status is available only for the group, but the explanatory variable is observed for each individual. However, for reasons such as the high cost of assays, the confidentiality of the patients, or the impossibility of measuring a concentration under a detection limit, the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid. We develop consistent parametric and nonparametric estimators of the conditional prevalence in this complex problem. We establish theoretical properties of our estimators and illustrate their practical performance on simulated and real data. We extend our techniques to the case where the group status is measured imperfectly, and to the setting where the covariate is aggregated and the individual status is available. Supplementary materials for this article are available online.

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions about the exogeneity of the covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given a certain number of predictors, namely, the distribution of the correlation of a response variable $Y$ with the best $s$ linear combinations of $p$ covariates $\mathbf{X}$, even when $\mathbf{X}$ and $Y$ are independent. When the covariance matrix of $\mathbf{X}$ possesses the restricted eigenvalue property, we derive such distributions for both a finite $s$ and a diverging $s$, using Gaussian approximation and empirical process techniques. However, such a distribution depends on the unknown covariance matrix of $\mathbf{X}$. Hence, we use the multiplier bootstrap procedure to approximate the unknown distributions and establish the consistency of such a simple bootstrap approach. The results are further extended to the situation where the residuals are from regularized fits. Our approach is then used to construct the upper confidence limit for the maximum spurious correlation and to test the exogeneity of the covariates. The former provides a baseline for guarding against false discoveries and the latter tests whether our fundamental assumptions for high-dimensional model selection are statistically valid. Our techniques and results are illustrated with both numerical examples and real data analysis.