We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact, the common assumption of linearity and/or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression. The semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example. This article has online supplementary material.

We recognize well the abilities of dendritic cells to activate effector T cell (Teff cell) responses to an array of antigens and think of these cells in this context as pre-eminent antigen-presenting cells, but dendritic cells are also critical to the induction of immunologic tolerance. Herein, we review our knowledge on the different kinds of tolerogenic or regulatory dendritic cells that are present or can be induced in experimental settings and humans, how they operate, and the diseases in which they are effective, from allergic to autoimmune diseases and transplant tolerance. The primary conclusions that arise from these cumulative studies clearly indicate that the agent(s) used to induce the tolerogenic phenotype and the status of the dendritic cell at the time of induction influence not only the phenotype of the dendritic cell, but also that of the regulatory T cell responses that they in turn mobilize. For example, while many, if not most, types of induced regulatory dendritic cells lead CD4+ naïve or Teff cells to adopt a CD25+Foxp3+ Treg phenotype, exposure of Langerhans cells or dermal dendritic cells to vitamin D leads in one case to the downstream induction of CD25+Foxp3+ regulatory T cell responses, while in the other to Foxp3− type 1 regulatory T cells (Tr1) responses. Similarly, exposure of human immature versus semi-mature dendritic cells to IL-10 leads to distinct regulatory T cell outcomes. Thus, it should be possible to shape our dendritic cell immunotherapy approaches for selective induction of different types of T cell tolerance or to simultaneously induce multiple types of regulatory T cell responses. This may prove to be an important option as we target diseases in different anatomic compartments or with divergent pathologies in the clinic. Finally, we provide an overview of the use and potential use of these cells clinically, highlighting their potential as tools in an array of settings.

In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the in¯uence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They con®rm the robustness properties of the new estimator. An S-Plus function for the highly robust autocovariance estimator is made available on the Web at http://www-math.mit.edu/ $ yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank.

Summary Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a minimum assumption on the specific regression form, it enjoys attractive advantages as well as encounters unique challenges in comparison with the variable selection approach. We review the current literature of dimension reduction with an emphasis on the two most popular models, where the dimension reduction affects the conditional distribution and the conditional mean, respectively. We discuss various estimation and inference procedures in different levels of detail, with the intention of focusing on their underneath idea instead of technicalities. We also discuss some unsolved problems in this area for potential future research.

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions. Our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods.