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It is known that there is a dichotomy in the performance of model selectors. Those that are consistent (having the oracle property) do not achieve the asymptotic minimax rate for prediction error. We look at this phenomenon closely, and argue that the set of parameters on which this dichotomy occurs is extreme, even pathological, and should not be considered when evaluating model selectors. We characterize this set, and show that, when such parameters are dismissed from consideration, consistency and asymptotic minimaxity can be attained simultaneously.
Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also use data to select a set of variables and construct the estimation rule using only the selected variables. In this work, we propose an asymptotically
We consider the problem of choosing between several models in least-squares regression with heteroscedastic data. We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least for some t
Discussion of Latent variable graphical model selection via convex optimization by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
This paper investigates the property of the penalized estimating equations when both the mean and association structures are modelled. To select variables for the mean and association structures sequentially, we propose a hierarchical penalized gener
We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We consider predicto