Related papers: Estimation in high-dimensional linear models with …

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…

Model-assisted regression estimation is fundamental in survey sampling for incorporating auxiliary information. However, when the auxiliary dimension grows with the sample size, the standard Generalized regression (GREG) estimator can…

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor…

We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…

For high-dimensional linear regression models, we review and compare several estimators of variances $\tau^2$ and $\sigma^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable.…

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…

The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units…

We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid…

As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…

In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function…

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…