非可识别性与相依性下的一致阶数选择

中文摘要 AI 辅助

我们为惩罚最小二乘程序提供了一致性的充分条件，该程序从一系列嵌套类中选择回归模型的阶数（维度），允许误差为相依的鞅差序列。主要贡献在于放宽了经典的可识别性要求：索引大于真实阶数的类的参数无需被识别，前提是额外的、多余的维度在真实参数附近允许对真实值进行线性逼近。这一放宽使得候选模型的数量可以随样本量增长，从而消除了通常所需的固定上界。我们验证了应用工作中使用的两类非线性回归模型所产生的高层条件：多机制平滑转换回归和具有通用广义线性模型专家的混合专家模型。在BIC型惩罚下，当候选模型的数量增长速度慢于样本量的对数时，所得阶数选择规则在任一模型类中都是一致的。

英文摘要

We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: parameters indexing classes larger than the true order need not be identified, provided the additional, excess directions admit a linear approximation to the truth in a neighbourhood of the true parameter. This relaxation lets the number of candidate models grow with the sample size, removing the usual need for a fixed upper bound. We verify the resulting high-level conditions for two classes of nonlinear regression models used in applied work: multiple-regime smooth transition regression and mixture-of-experts models with generic generalized linear model experts. Under a BIC-type penalty, the resulting order selection rule is consistent in either model class whenever the number of candidate models grows slower than the logarithm of the sample size.

发表机构

• Getulio Vargas Foundation（恩里克·加斯帕尔·杜特雷基金会）

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