Related papers: Targeted Principal Components Regression
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
We study regression using functional predictors in situations where these functions contain both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can…
We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized…
This paper considers linear panel data models where the dependence of the regressors and the unobservables is modelled through a factor structure. The asymptotic setting is such that the number of time periods and the sample size both go to…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…
We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the…
Given a data matrix $\mathbf{A} \in \mathbb{R}^{n \times d}$, principal component projection (PCP) and principal component regression (PCR), i.e. projection and regression restricted to the top-eigenspace of $\mathbf{A}$, are fundamental…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…
This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
We propose a new method for statistical inference in generalized linear models. In the overparameterized regime, Principal Component Regression (PCR) reduces variance by projecting high-dimensional data to a low-dimensional principal…
With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear…