Related papers: Dimension Reduction and MARS
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…
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…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
It is often of interest to estimate regression functions non-parametrically. Penalized regression (PR) is one statistically-effective, well-studied solution to this problem. Unfortunately, in many cases, finding exact solutions to PR…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…
Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration…
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,…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…
A new method of Hansen solubility parameters (HSPs) prediction was developed by combining the multivariate adaptive regression splines (MARSplines) methodology with a simple multivariable regression involving 1D and 2D PaDEL molecular…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…