Factor models and variable selection in high-dimensional regression analysis

By Alois Kneip, Pascal Sarda. 2011

52 citations recorded by the source corpus.

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach: it is assumed that the predictor vector can be decomposed into a sum of two uncorrelated random components reflecting common factors and specific variabilities of the explanatory variables. It is shown that the traditional assumption of a sparse vector of parameters is restrictive in this context. Common factors may possess a significant influence on the response variable which cannot be captured by the specific effects of a small number of individual variables. We therefore propose to include principal components as additional explanatory variables in an augmented regression model. We give finite sample inequalities for estimates of these components. It is then shown that model selection procedures can be used to estimate the parameters of the augmented model, and we derive theoretical properties of the estimators. Finite sample performance is illustrated by a simulation study.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5baea52329151cbd7e8a4729ea93f6b775169b8f

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Variable selection in functional data classification: a maxima-hunting proposal (2013, background): “s \sparse" or \sparsity" to describe situations in which variable selection is the rst natural aim; see e.g., Gertheiss and Tutz (2010) and Rosasco et al. (2013). It has been also argued in Kneip and Sarda (2011) that the standard sparsity models are sometimes too restrictive so that it is”
Functional Data Analysis (2016, methodology): “…covariates, such as modeling predictor times that exercise an individual predictor eﬀect on an outcome that goes beyond the functional linear model (Kneip & Sarda 2011), predictor selection among high-dimensional functional principal component scores and baseline covariates in functional…”