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In statistics and machine learning, we are interested in the eigenvectors (or singular vectors) of certain matrices (eg covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. The Davis-Kahan sin theorem is often used to bound the difference between the eigenvectors of a matrix A and those of a perturbed matrix A= A+ E, in terms of l2 norm. In this paper, we prove that when A is a low-rank and incoherent matrix, the l norm perturbation bound of singular vectors (or eigenvectors in the symmetric case) is smaller by a factor of

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This new regime allows high dimensionality and diverging eigenvalue spikes and provides new insights into the roles the leading eigenvalues, sample size, and dimensionality play in principal component analysis. The results are proven by a technical device, which swaps the role of rows and columns and converts the high-dimensional problems into low-dimensional ones. Our results are a natural extension of those in Paul (2007) to more general setting with new insights and solve the rates of convergence problems in Shen et al.(2013). They also reveal the biases of the estimation of leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.

Stem cell therapies have had tremendous potential application for many diseases in recent years. However, the tumorigeneic properties of stem cells restrict their potential clinical application; therefore, strategies for reducing the tumorigenic potential of stem cells must be established prior to transplantation. We have demonstrated that syngeneic transplantation of embryonic stem cells (ESCs) provokes an inflammatory response that involves the rapid recruitment of bone marrow-derived macrophages (BMDMs). ESCs are able to prevent mature macrophages from macrophage colony-stimulating factor (M-CSF) withdrawal-induced apoptosis, and thus prolong macrophage lifespan significantly by blocking various apoptotic pathways in an M-CSF-independent manner. ESCs express and secrete IL-34 which may be responsible for ESC-promoted macrophage survival. This anti-apoptotic effect of ESCs involves activation of extracellular signal-regulated kinase (ERK)1/2 and PI3K/Akt pathways and thus, inhibition of ERK1/2 and PI3K/AKT activation decreases ESC-induced macrophage survival. Functionally, ESC-treated macrophages also showed a higher level of phagocytic activity. ESCs further serve to polarize BMDMs into M2-like macrophages that exhibit most tumor-associated macrophage (TAM) phenotypic and functional features. ESC-educated macrophages produce high levels of arginase-1, Tie-2 and TNF-, which participate in angiogenesis and contribute to teratoma progression. Our study suggests that induction of M2-like macrophage activation is an important mechanism for teratoma development. Strategies targeting macrophages to

We examine the effect of errors in covariates in nonparametric function estimation. These functions include densities, regressions and conditional quantiles. To estimate these functions, we use the idea of deconvoluting kernels in conjunction with the ordinary kernel methods. We also discuss a new class of function estimators based on local polynomials.

This paper studies hypothesis testing and parameter estimation in the context of the divide-and-conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from k subsamples of size n/k, where n is the sample size. In both low dimensional and sparse high dimensional settings, we address the important question of how large k can be, as n grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as an oracle with access to the full sample. Thorough numerical results are provided to back up the theory.

This paper is concerned with the problem of top- K ranking from pairwise comparisons. Given a collection of K items and a few pairwise comparisons across them, one wishes to identify the set of K items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model---the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress towards characterizing the performance (eg the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top- K ranking remains unsettled.

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the <i>curse of dimensionality</i>, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility matrix in the time domain and in the state domain. Asymptotic normality is separately established for nonparametric estimators in the time domain and state domain. These two estimators are asymptotically independent. Hence, they can be combined, through a dynamic weighting scheme, to improve the efficiency of volatility matrix estimation. The optimal dynamic weights are derived, and it is shown that the aggregated estimator uniformly dominates volatility matrix estimators using time-domain or state-domain smoothing alone. A simulation study, based on an essentially affine model for the term structure, is

We develop a specification test for the transition density of a discretely-sampled continuous-time diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts assumed by the null hypothesis. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are critically investigated via simulation studies and are compared with other tests. Our approaches are illustrated by applications to implied volatility data and Treasury bill data.

Past, Present, and Future of Statistical Science was commissioned in 2013 by the Committee of Presidents of Statistical Societies (COPSS) to celebrate its 50th anniversary and the International Year of Statistics. COPSS consists of five charter member statistical societies in North America and is best known for sponsoring prestigious awards in stat

Tumor growth and metastasis require that tumor cells must have either the potential to shift genetically or epigenetically between proliferative and invasive phenotypes or both phenotypes simultaneously. In the present study, we demonstrated that neuroblastoma growth and invasion were distinct processes that were carried out by proliferative and invasive phenotypes of tumor cells, respectively. Two subpopulations from human neuroblastoma cell line were isolated: highly invasive (HI) cells and low-invasive (LI) cells. HI and LI cells had different proliferative rate and metastatic ability <i>in vitro</i> and <i>in vivo</i> . In addition, they had distinct activated signal pathways and sensitivities to chemotherapy drugs. Affymetrix microarray and quantitative reverse transcriptasepolymerase chain reaction revealed that visinin-like protein-1 (VSNL-1) mRNA in HI cells was significantly higher than