Abstract:
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We introduce a new class of prior distributions for linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression R-squared. This is then distributed to the coefficients conditional on the value of R-squared. In addition to a convenient interpretation, compared to existing shrinkage priors, we show that the use of this prior can provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals.
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