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Local Spectral Analysis of Qualitative Sequences via Minimum Description Length

In: Robust and Multivariate Statistical Methods

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  • David S. Stoffer

    (University of Pittsburgh, Department of Statistics)

Abstract

The idea of signal detection in the frequency domain for qualitative-valued time series was developed in Stoffer et al. (Biometrika 80(3):611–622, 1993) under the assumption of homogeneity. The tool is called the spectral envelope and is related to the concept of scaling qualitative data. After reviewing the basic ideas, we present a method for fitting a local spectral envelope to heterogeneous sequences based on a minimum description length (MDL) criterion for choosing the best fitting model based on parsimony. Inherent in the methodology is the detection of breakpoints in long sequences. Because the search space is immense, optimization is accomplished via a genetic algorithm (GA) to effectively tackle the problem. Numerical examples are given using sleep state data and DNA sequences.

Suggested Citation

  • David S. Stoffer, 2023. "Local Spectral Analysis of Qualitative Sequences via Minimum Description Length," Springer Books, in: Mengxi Yi & Klaus Nordhausen (ed.), Robust and Multivariate Statistical Methods, pages 477-495, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-22687-8_22
    DOI: 10.1007/978-3-031-22687-8_22
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