This article studies estimation of partially linear hazard regression models for multivariate survival data. A profile pseudopartial likelihood estimation method is proposed under the marginal hazard model framework. The estimation on the parameters for the linear part is accomplished by maximization of a pseudopartial likelihood profiled over the nonparametric part. This enables us to obtain-consistent estimators of the parametric component. Asymptotic normality is obtained for the estimates of both the linear and nonlinear parts. The new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit. An algorithm of fast implementation of our proposed method is presented. Consistent standard error estimates using sandwich-type ideas are also developed, which facilitates inferences for the model. It is shown that the

Data subject to heavytailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultrahigh dimensional settings with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate (RA) quadratic loss will be called the RA lasso. In the ultrahigh dimensional setting, where the dimensionality can grow exponentially with the sample size

Economists historically measure the degree to which the market is surprised by an earnings announcement by the consensus forecast error, defined as difference between the actual earnings and the consensus forecast. The consensus might be calculated using either the mean or median of security analysts forecasts. The premise of this measure is that the consensus forecast is a good proxy for the markets expectation of earnings. Hence the consensus forecast error captures how surprised the market is when the earnings is announced. The consensus forecast error is a building block of a host of studies across finance, accounting and economics (see for a survey of event studies in Kothari (2001)). For instance, in finance and accounting, it is used in event studies of how efficiently markets react to earnings announcements. Efficient market studies when it comes to bond or currency markets and macroeconomic

Multiple hypothesis testing is a fundamental problem in high-dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any single-nucleotide polymorphisms (SNPs) are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In this article, we propose a novel method—based on principal factor approximation—that successfully subtracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure.We derive an approximate expression for false discovery proportion (FDP) in large-scale multiple testing when a common threshold is used and provide a consistent estimate of realized FDP. This result has important applications in controlling false discovery rate and FDP. Our estimate of realized FDP compares favorably with Efron’s approach, as demonstrated in the simulated examples. Our approach is further illustrated by some real data applications. We also propose a dependence-adjusted procedure that is more powerful than the fixed-threshold procedure. Supplementary material for this article is available online.

In statistics and machine learning, people are often 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. One usually employs Davis-Kahan \sin theorem to bound the difference between the eigenvectors of a matrix \sin and those of a perturbed matrix \sin , in terms of \sin norm. In this paper, we prove that when \sin is a low-rank and incoherent matrix, the \sin norm perturbation bound of singular vectors (or eigenvectors in the symmetric case) is smaller by a factor of \sin or \sin for left and right vectors, where \sin and \sin are the matrix dimensions. The power of this new perturbation result is shown in robust covariance estimation, particularly when random variables have heavy tails. There, we propose new robust covariance estimators and establish their asymptotic properties using the newly developed perturbation bound. Our theoretical results are verified through extensive numerical experiments.