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- W2905232221 abstract "We demonstrate that, in a regression setting with a Hilbertian predictor, a response variable is more likely to be more highly correlated with the leading principal components of the predictor than with trailing ones. This is despite the extraction procedure being unsupervised. Our results are established under the conditional independence model, which includes linear regression and single-index models as special cases, with some assumptions on the regression vector. These results are a generalisation of earlier work which showed that this phenomenon holds for predictors which are real random vectors. A simulation study is used to quantify the phenomenon." @default.
- W2905232221 created "2018-12-22" @default.
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- W2905232221 date "2018-12-06" @default.
- W2905232221 modified "2023-10-16" @default.
- W2905232221 title "On principal components regression with Hilbertian predictors" @default.
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- W2905232221 doi "https://doi.org/10.1007/s10463-018-0702-9" @default.
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