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Envelope Models in Gaussian Copula Regression and High-dimensional Hypothesis Testing

  • Author / Creator
    Wei Tu
  • Envelopes, introduced by Cook et al. (2007), encompass a class of methods for increasing efficiency in multivariate analyses without altering traditional objectives. Envelopes have been successfully incorporated to a variety of regression models from generalized linear models to quantile regression. Despite the potential of achieving substantial efficiency gains, inference based on an envelope is not invariant under rescaling and other transformation of the variables. Furthermore, envelopes have mostly been studied in the context of regression, but not hypothesis testing. This thesis mainly contains three parts. In the first part, we develop adaptive estimation and inference methods for envelope models that achieve the same performance without the knowledge of the marginal transformations of the responses and predictors in the context of response envelopes. In the second part, we study predictor envelopes and sparse envelopes. Using a Kendall's tau based covariance matrix estimator and the scaled envelope models, we propose an envelope-based Gaussian copula estimator. In the third part of the thesis, we propose an envelope-based high-dimensional multivariate test for mean vector that can efficiently exploit the dependency structures within the high-dimensional vector. In all three parts, theoretical properties of the procedures are studied, and extensive simulation studies and data analysis have been conducted to illustrate the usefulness of the proposed procedures in practice.

  • Subjects / Keywords
  • Graduation date
    Spring 2021
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-97a0-wt31
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.