Inference of high-dimensional linear models with time-varying coefficients

Xiaohui Chen, Yifeng He

Research output: Contribution to journalArticlepeer-review


We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge regression estimator. Due to the non-stationarity feature of the model, dynamic bias-variance decomposition of the estimator is obtained. With a bias-correction procedure, the local null distribution of the estimator of the time-varying coefficient vector is characterized for iid Gaussian and heavy-tailed errors. The limiting null distribution is also established for Gaussian process errors, and we show that the asymptotic properties differ between short-range and long-range dependent errors. Here, p-values are adjusted by a Bonferroni-type correction procedure to control the familywise error rate (FWER) in the asymptotic sense at each time point. The finite sample size performance of the proposed inference algorithm is illustrated with synthetic data and an application to learn brain connectivity by using the resting-state fMRI data for Parkinson's disease.

Original languageEnglish (US)
Pages (from-to)255-276
Number of pages22
JournalStatistica Sinica
Issue number1
StatePublished - Jan 2018


  • Asymptotic theory
  • High-dimensional linear models
  • Statistical inference
  • Time series analysis
  • Time-varying coefficients

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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