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近奇异设计下的收缩估计AI 解读

Shrinkage estimation procedures such as ridge regression and the lasso have been proposed for stabilizing estimation in linear models when high collinearity exists in the design. In this paper, we consider asymptotic properties of shrinkage estimators in the case of “nearly singular” designs.I thank Hannes Leeb and Benedikt Pötscher and also the referees for their valuable comments. This research was supported by a grant from the Natural Sciences and Engineering Research…

通过融合 Lasso 实现稀疏性与平滑性AI 解读

Summary The lasso penalizes a least squares regression by the sum of the absolute values (L1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients equal to 0). We propose the ‘fused lasso’, a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the L1-norm of both the coefficients and their successive differences. Thus it encourages sparsity of the…

Lasso 型估计量的渐近性质AI 解读

We consider the asymptotic behavior ofregression estimators that minimize the residual sum of squares plus a penalty proportional to $\sum|\beta_j|^{\gamma}$. for some $\gamma > 0$. These estimators include the Lasso as a special case when $\gamma = 1$. Under appropriate conditions, we show that the limiting distributions can have positive probability mass at 0 when the true value of the parameter is 0.We also consider asymptotics for “nearly singular” designs.

自适应模型选择的协方差膨胀准则AI 解读

Summary We propose a new criterion for model selection in prediction problems. The covariance inflation criterion adjusts the training error by the average covariance of the predictions and responses, when the prediction rule is applied to permuted versions of the data set. This criterion can be applied to general prediction problems (e.g. regression or classification) and to general prediction rules (e.g. stepwise regression, tree-based models and neural nets). As a…

一般条件下L₁回归估计量的极限分布AI 解读

It is well known that $L_1$-estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0. In this paper, we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0.

无限方差误差下动态线性回归模型的估计AI 解读

This paper considers the asymptotic behavior of M -estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n −½ rate.

无限方差创新的积分过程中的 M 估计极限理论AI 解读

We consider the limiting distributions of M -estimates of an “autoregressive” parameter when the observations come from an integrated linear process with infinite variance innovations. It is shown that M -estimates are, asymptotically, infinitely more efficient than the least-squares estimator (in the sense that they have a faster rate of convergence) and are conditionally asymptotically normal.

无限方差情形下样本均值的自助法AI 解读

Athreya showed that the bootstrap distribution of a sum of infinite variance random variables did not (with probability 1) tend weakly to a fixed distribution but instead tended in distribution to a random distribution. In this paper, we give a different proof of Athreya's result motivated by a heuristic large sample representation of the bootstrap distribution.

无限方差自回归过程下赤池信息准则的一致性AI 解读

Suppose $\{X_n\}$ is a $p$th order autoregressive process with innovations in the domain of attraction of a stable law and the true order $p$ unknown. The estimate $\hat{p}$ of $p$ is chosen to minimize Akaike's information criterion over the integers $0, 1, \cdots, K$. It is shown that $\hat{p}$ is weakly consistent and the consistency is retained if $K \rightarrow \infty$ as $N \rightarrow \infty$ at a certain rate depending on the index of the stable law.