Related papers: Estimation of multiple mean vectors in high dimens…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting…
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…
A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Hazard ratios are frequently reported in time-to-event and epidemiological studies to assess treatment effects. In observational studies, the combination of propensity score weights with the Cox proportional hazards model facilitates the…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…