Related papers: High-Dimensional Hettmansperger-Randles Estimator …
When multiple models are considered in regression problems, the model averaging method can be used to weigh and integrate the models. In the present study, we examined how the goodness-of-prediction of the estimator depends on the…
In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
Density estimation plays a key role in many tasks in machine learning, statistical inference, and visualization. The main bottleneck in high-dimensional density estimation is the prohibitive computational cost and the slow convergence rate.…
In this paper we derive the optimal linear shrinkage estimator for the high-dimensional mean vector using random matrix theory. The results are obtained under the assumption that both the dimension $p$ and the sample size $n$ tend to…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…
In a landmark result, Chen et al. (2018) showed that multivariate medians induced by halfspace depth attain the minimax optimal convergence rate under Huber contamination and elliptical symmetry, for both location and scatter estimation. We…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
This paper proposes a desparsified GMM estimator for estimating high-dimensional regression models allowing for, but not requiring, many more endogenous regressors than observations. We provide finite sample upper bounds on the estimation…
This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…
This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general…
Learning high-dimensional distributions is an important yet challenging problem in machine learning with applications in various domains. In this paper, we introduce new techniques to formulate the problem as solving Fokker-Planck equation…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…