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Multiplier and empirical subsample bootstraps for maxima in high dimensional time series analysis

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  • Ma, Ruru
  • Zhang, Shibin

Abstract

The distribution of maxima is crucial for simultaneous inference of high dimensional parameters. This paper focuses on the bootstrap approximation to the distribution of maxima in high dimensional time series analysis. We propose two novel approaches, the multiplier subsample bootstrap (MSB) and the empirical subsample bootstrap (ESB), to approximate the distribution of maxima constructed from high dimensional time series. Both approaches utilize block-based subsample statistics to build the bootstrap statistics. The MSB assigns weights to block-based subsample statistics using random elements, while the ESB resamples from them independently and uniformly. Under certain regularity conditions, we establish the asymptotic validity of the two proposed approaches, when the parameter dimension is large or even much larger than the sample size. A simulation study demonstrates that both the MSB and ESB perform well.

Suggested Citation

  • Ma, Ruru & Zhang, Shibin, 2026. "Multiplier and empirical subsample bootstraps for maxima in high dimensional time series analysis," Journal of Multivariate Analysis, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:jmvana:v:213:y:2026:i:c:s0047259x25001745
    DOI: 10.1016/j.jmva.2025.105579
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