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Ultra High Dimension Variable Selection with Threshold Partial Correlations

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2022, Doctor of Philosophy (Ph.D.), Bowling Green State University, Statistics.
With respect to variable selection in linear regression, partial correlation for normal models (Buhlmann, Kalisch and Maathuis, 2010), was a powerful alternative method to penalized least squares approaches (LASSO, SCAD, etc.). The method was improved by Li, Liu, Lou (2015) with the concept of threshold partial correlation (TPC) and extension to elliptical contoured dis- tributions. The TPC procedure is endowed with its dominant advantages over the simple partial correlation in high or ultrahigh dimensional cases (where the dimension of predictors increases in an exponential rate of the sample size). However, the convergence rate for TPC is not very satis- fying since it usually takes substantial amount of time for the procedure to reach the final solution, especially in high or even ultrahigh dimensional scenarios. Besides, the model assumptions on the TPC are too strong, which suggest the approach might not be conveniently used in practice. To address these two important issues, this dissertation puts forward an innovative model selection al- gorithm. It starts with an alternative definition of elliptical contoured distributions, which restricts the impact of the marginal kurtosis. This posts a relatively weaker condition for the validity of the model selection algorithm. Based on the simulation results, the new approach demonstrates not only competitive outcomes with established methods such as LASSO and SCAD, but also advan- tages in terms of computing efficiency. The idea of the algorithm is extended to survival data and nonparametric inference by exploring various measurements on correlations between the response variable and predictors.
John Chen, Ph.D. (Committee Chair)
Arrigo Michael, Ph.D. (Other)
Hanfeng Chen, Ph.D. (Committee Member)
Wei Ning, Ph.D. (Committee Member)
78 p.

Recommended Citations

Citations

  • Liu, Y. (2022). Ultra High Dimension Variable Selection with Threshold Partial Correlations [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1656881820635115

    APA Style (7th edition)

  • Liu, Yiheng. Ultra High Dimension Variable Selection with Threshold Partial Correlations. 2022. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1656881820635115.

    MLA Style (8th edition)

  • Liu, Yiheng. "Ultra High Dimension Variable Selection with Threshold Partial Correlations." Doctoral dissertation, Bowling Green State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1656881820635115

    Chicago Manual of Style (17th edition)