Related papers: Deciding the dimension of effective dimension redu…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension…
In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables--for…
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.…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for…
Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…