On distribution-weighted partial least squares with diverging number of highly correlated predictors

Li Ping Zhu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover directions in the central subspace, then use the distribution-weighted least squares estimator as a seed vector and project it onto a Krylov space by partial least squares to avoid computing the inverse of the covariance of predictors. Thus, distrbution-weighted partial least squares can handle the cases with high dimensional and highly correlated predictors. Furthermore, we also suggest an iterative algorithm for obtaining a better initial value before implementing partial least squares. For theoretical investigation, we obtain strong consistency and asymptotic normality when the dimension p of predictors is of convergence rate O[n1/2/ log (n)] and o(n1/3) respectively where n is the sample size. When there are no other constraints on the covariance of predictors, the rates n1/2 and n1/3 are optimal. We also propose a Bayesian information criterion type of criterion to estimate the dimension of the Krylov space in the partial least squares procedure. Illustrative examples with a real data set and comprehensive simulations demonstrate that the method is robust to non-ellipticity and works well even in 'small n-large p' problems.

Original languageEnglish
Pages (from-to)525-548
Number of pages24
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume71
Issue number2
DOIs
Publication statusPublished - Apr 2009

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central subspace
  • Collinearity
  • Distribution function
  • Inverse regression
  • Least squares estimation
  • Partial least squares

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