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Skew-normal antedependence models for skewed longitudinal data

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  • Shu-Ching Chang
  • Dale L. Zimmerman

Abstract

Antedependence models, also known as transition models, have proven to be useful for longitudinal data exhibiting serial correlation, especially when the variances and/or same-lag correlations are time-varying. Statistical inference procedures associated with normal antedependence models are well-developed and have many nice properties, but they are not appropriate for longitudinal data that exhibit considerable skewness. We propose two direct extensions of normal antedependence models to skew-normal antedependence models. The first is obtained by imposing antedependence on a multivariate skew-normal distribution, and the second is a sequential autoregressive model with skew-normal innovations. For both models, necessary and sufficient conditions for $p$th-order antedependence are established, and likelihood-based estimation and testing procedures for models satisfying those conditions are developed. The procedures are applied to simulated data and to real data from a study of cattle growth.

Suggested Citation

  • Shu-Ching Chang & Dale L. Zimmerman, 2016. "Skew-normal antedependence models for skewed longitudinal data," Biometrika, Biometrika Trust, vol. 103(2), pages 363-376.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:2:p:363-376.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw006
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Wang, Sheng & Zimmerman, Dale L. & Breheny, Patrick, 2020. "Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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