2017/02/23 by Jonathan Williams, Williams, Jonathan P, Jan Hannig +1 · 1 citation
Mathematics · Decision Sciences · Engineering · #Statistical Methods and Inference #Probabilistic and Robust Engineering Design #Control Systems and Identification
paper · pdf · doi:10.48550/arxiv.1702.07283
Standard penalized methods of variable selection and parameter estimation\nrely on the magnitude of coefficient estimates to decide which variables to\ninclude in the final model. However, coefficient estimates are unreliable when\nthe design matrix is collinear. To overcome this challenge an entirely new\nperspective on variable selection is presented within a generalized fiducial\ninference framework. This new procedure is able to effectively account for\nlinear dependencies among subsets of covariates in a high-dimensional setting\nwhere p can grow almost exponentially in n, as well as in the classical\nsetting where p \≤ n. It is shown that the procedure very naturally assigns\nsmall probabilities to subsets of covariates which include redundancies by way\nof explicit L0 minimization. Furthermore, with a typical sparsity\nassumption, it is shown that the proposed method is consistent in the sense\nthat the probability of the true sparse subset of covariates converges in\nprobability to 1 as n \→ \∞, or as n \→ \∞ and p \→ \∞.\nVery reasonable conditions are needed, and little restriction is placed on the\nclass of possible subsets of covariates to achieve this consistency result.\n