We derive upper bounds for random design linear regression with dependent ($\beta$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem -- the noise level of the problem -- and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

翻译：本文针对无任何可实现性假设的随机设计线性回归（数据满足$\beta$-混合依赖）推导了上界。与严格可实现鞅噪声情形不同，文献中尚未给出实例最优的非渐近精确结果。在最优化常数因子意义上，我们的分析正确再现了中心极限定理所预测的方差项——即该问题的噪声水平——从而在引入模型误设时展现出优雅的性能退化。经过初始烧期后，该结果在中等偏差范围内达到精确，尤其不会因混合时间因子而放大主导阶项。