Related papers: Reducing Subspace Models for Large-Scale Covarianc…
We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each group and sharing information about the space…
Envelope model also known as multivariate regression model was proposed to solve the multiple response regression problems. It measures the linear association between predictors and multiple responses by using the minimal reducing subspace…
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…
Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…
When multiple measures are collected repeatedly over time, redundancy typically exists among responses. The envelope method was recently proposed to reduce the dimension of responses without loss of information in regression with…
Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Envelope method was recently proposed as a method to reduce the dimension of responses in multivariate regressions. However, when there exists missing data, the envelope method using the complete case observations may lead to biased and…
This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…
Small area estimation has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression,…
This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Envelope methodology is succinctly pitched as a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives \citep[first sentence of page 1]{cook2018introduction}. This description is true…
Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
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…
Envelope methods improve the estimation efficiency in multivariate linear regression by identifying and separating the material and immaterial parts of the responses or the predictors and estimating the regression coefficients using only…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…