arXiv 11 Mar 2021 · Mathematics — Statistics Theory
arXiv:2103.06691 · PDF · DOI · OpenAlex · Extracted main text
Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. As a special case, principal loading analysis discards variables that are not correlated with the remaining ones. In multivariate linear regression on the other hand, predictors that are neither correlated with both the remaining predictors nor with the dependent variables have a regression coefficients equal to zero. Hence, if the goal is to select a number of predictors, variables that do not correlate are discarded as it is also done in principal loading analysis. That both methods select the same variables occurs not only for the special case of zero correlation however. We contribute conditions under which both methods share the same variable selection. Further, we extend those conditions to provide a choice for the threshold in principal loading analysis which only follows recommendations based on simulation results so far.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bauer, J. O., Drabant, B (2021) Principal loading analysis self | 0.961 | 9 | 7 | 89% |
| 2 | Bauer, J. O (2021) Correlation based principal loading analysis self | 0.644 | 2 | 2 | 100% |
| 3 | Neudecker, H., Wesselman, A (1990) The asymptotic variance matrix of the sample correlation matrix | 0.511 | 2 | 2 | 50% |
| 4 | Stewart, G. W., Sun, J (1990) Matrix perturbation theory | 0.511 | 2 | 2 | 50% |
| 5 | Yu, Y., Wang, T., Samworth, R. J (2015) A useful variant of the Davis–Kahan theorem for statisticians | 0.511 | 2 | 2 | 50% |
| 6 | Anderson, T. W (1963) Asymptotic theory for principal component analysis | 0.405 | 1 | 1 | 100% |
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| 8 | Dauxois, J., Pousse, A., Romain, Y (1982) Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference | 0.405 | 1 | 1 | 100% |
| 9 | Hawkins, D. M (1973) On the investigation of alternative regressions by principal component analysis | 0.405 | 1 | 1 | 100% |
| 10 | Hotelling, H (1933) Analysis of a complex of statistical variables into principal components | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 21 scored citations.