- Restrictions on Access:
- Restricted (PSU Only).
- In recent years, power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics. Many scientific research questions can be converted into hypothesis testing problems, for example, the discovery of association between gene-sets and disease outcomes, the evaluation on the validity of a pricing model for financial market. Various tests possess different high-power regions. In practice, we may lack prior knowledge about the alternatives when testing for a problem of interest. It is important to develop powerful testing procedures against more general alternatives. In this dissertation, we propose new methods to achieve power enhancement (PE) in tests for high-dimensional data. In particular, we consider the problem of enhancing test power in three topics: (1) a one-sample test on multi-factor pricing models for large panels, (2) a two-sample test on the equality of high-dimensional covariance matrices, and (3) a simultaneous test on the equality of two-sample mean vectors and covariance matrices of high-dimensions. Methodologically, we provide a new perspective to the literature by studying and utilizing the asymptotic joint distribution of different statistics. We show two PE techniques of (i) aggregating information via the combination of p-values, and (ii) constructing PE components, to achieve enhanced test power in two aspects: (a) expanding high-power regions towards a wider alternative space with respect to one parameter of interest, and (b) expanding test capability to alternative spaces with respect to more parameters. Theoretically, we derive joint limiting laws of the corresponding test statistics. We prove that the proposed power-enhanced tests achieve the desired PE properties following the guidance of the three general PE principles (Fan, Liao and Yao, 2015). Practically, the test efficacy is demonstrated by Monte Carlo simulations as well as empirical studies on testing market efficiency and identifying differentially expressed gene-sets.
- Dissertation Note:
- Ph.D. Pennsylvania State University 2021.
- Technical Details:
- The full text of the dissertation is available as an Adobe Acrobat .pdf file ; Adobe Acrobat Reader required to view the file.
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