This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. When the dimensionality is large, the factors can be estimated accurately even when the sample size is finite. We propose a flexible semi-parametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The covariates effects on the factor loadings are further

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio (SELR) tests. The approach is also applied to test conditional estimating equations on the distributions of stochastic errors. It is shown that the proposed SELR statistics follow asymptotically rescaled 2-distributions, with the scale constants and the degrees of freedom being independent of the nuisance parameters. This demonstrates that the Wilks phenomenon observed in Fan, Zhang and Zhang [Ann. Statist. 29

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimensional classification (Tibshirani et al., 2003). Within the context of the linear model, Fan and Lv (2008) showed that this simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iteratively sure independent screening (ISIS), is needed when the features are marginally unrelated but jointly related to the response variable. In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process. Our technique allows us to select important features in high-dimensional classification where the popularly used two-sample t-method fails. A new technique is introduced to reduce the false discovery rate in the feature screening stage. Several simulated and two real data examples are presented to illustrate the methodology.

Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-in-variable regression, including local polynomial estimation of derivative functions.

Inflammatory response following central nervous system (CNS) injury contributes to progressive neuropathology and reduction in functional recovery. Axons are sensitive to mechanical injury and toxic inflammatory mediators, which may lead to demyelination. Although it is well documented that degenerated myelin triggers undesirable inflammatory responses in autoimmune diseases such as multiple sclerosis (MS) and its animal model, experimental autoimmune encephalomyelitis (EAE), there has been very little study of the direct inflammatory consequences of damaged myelin in spinal cord injury (SCI), i.e., there is no direct evidence to show that myelin debris from injured spinal cord can trigger undesirable inflammation in vitro and in vivo. Our data showed that myelin can initiate inflammatory responses in vivo, which is complement receptor 3 (CR3)-dependent via stimulating macrophages to express pro-inflammatory molecules and down-regulates expression of anti-inflammatory cytokines. Mechanism study revealed that myelin-increased cytokine expression is through activation of FAK/PI3K/Akt/NF-B signaling pathways and CR3 contributes to myelin-induced PI3K/Akt/NF-B activation and cytokine production. The myelin induced inflammatory response is myelin specific as sphingomyelin (the major lipid of myelin) and myelin basic protein (MBP, one of the major proteins of myelin) are not able to activate NF-B signaling pathway. In conclusion, our results demonstrate a crucial role of myelin as an endogenous inflammatory stimulus that induces pro-inflammatory responses and suggest that blocking myelin-CR3 interaction and