B2028
Title: Projection inference for high-dimensional covariance matrices with structured shrinkage targets
Authors: Fabian Mies - Delft University of Technology (Netherlands) [presenting]
Ansgar Steland - RWTH Aachen (Germany)
Abstract: Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points. Inference for large covariance matrices is especially difficult due to noise accumulation, resulting in singular estimates and poor power of related tests. The singularity of the sample covariance matrix can be overcome by a linear combination with a structured target matrix, typically of diagonal form. We consider covariance shrinkage towards structured nonparametric estimators of the bandable or Toeplitz type, respectively, aiming at improved estimation accuracy and statistical power of tests even under nonstationarity. We derive feasible Gaussian approximation results for bilinear projections of the shrinkage estimators, which are valid under nonstationarity and dependence. These approximations enable us to formulate a statistical test for structural breaks in the marginal covariance structure of high-dimensional time series without restrictions on the dimension, and which is robust against nonstationarity of nuisance parameters. We show via simulations that shrinkage helps to increase the power of the proposed tests. Moreover, we suggest a data-driven choice of the shrinkage weights, and assess its performance by means of a Monte Carlo study. The results indicate that the proposed shrinkage estimator is superior for non-Toeplitz covariance structures close to fractional Gaussian noise.
