CONSISTENT AND CONSERVATIVE MODEL SELECTION WITH THE ADAPTIVE LASSO IN STATIONARY AND NONSTATIONARY AUTOREGRESSIONS
研究了自适应Lasso在平稳与非平稳自回归中的Oracle性质，证明其能一致选择模型并区分平稳与非平稳，同时探讨了BIC调参下的一致性与保守性模型选择对收缩备择假设的检验功效。
We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if only these had been included in the model from the outset. In particular, this implies that it is able to discriminate between stationary and nonstationary autoregressions and it thereby constitutes an addition to the set of unit root tests. Next, and important in practice, we show that choosing the tuning parameter by Bayesian Information Criterion (BIC) results in consistent model selection. However, it is also shown that the adaptive Lasso has no power against shrinking alternatives of the form c/T if it is tuned to perform consistent model selection. We show that if the adaptive Lasso is tuned to perform conservative model selection it has power even against shrinking alternatives of this form and compare it to the plain Lasso.