UNLOCKING THE REGRESSION SPACE
拓展回归模型的适用空间AI 解读 ↓
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拓展回归模型的适用空间AI 解读 ↓
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This article introduces and analyzes a framework that accommodates general heterogeneity in regression modeling. It demonstrates that regression models with fixed or time-varying parameters can be estimated using the ordinary least squares (OLS) and time-varying OLS methods, respectively, across a broad class of regressors and noise processes not covered by existing theory. The proposed setting facilitates the development of asymptotic theory and the estimation of robust standard errors. The robust confidence interval estimators accommodate substantial heterogeneity in both regressors and noise. The resulting robust standard error estimates coincide with White’s (1980, Econometrica 48 , 817–838) heteroskedasticity-consistent estimator but are applicable to a broader range of conditions, including models with missing data. They are computationally simple and perform well in Monte Carlo simulations. Their robustness, generality, and ease of implementation make them highly suitable for empirical applications. Finally, the article provides a brief empirical illustration.
对哪个目标量最好?时变处理的纵向匹配与目标试验模拟已知真值基准
On a non-collapsible survival mechanism, longitudinal-matching and target-trial-emulation methods are not competing estimators of one truth but answers to different causal questions, so a benchmark that scores them against a single "true hazard ratio" fabricates bias. We provide the direct comparison of relative efficiency, variance estimation, and model sensitivity that reviews find lacking. On a deliberately non-collapsible continuous-time Cox mechanism with known truth,…
带动量与非收敛自适应预条件的 SA-Adam 的 Polyak-Ruppert 中心极限定理
Adaptive optimizers combining preconditioning, momentum, and weight decay (Adam and AdamW) are, under Polyak-Ruppert averaging, candidate engines for one-pass inference. Does the averaged iterate keep the classical Polyak-Ruppert central limit theorem (CLT), with sandwich covariance $H^{-1}SH^{-1}$ (Hessian $H$, gradient covariance $S$), under momentum and non-convergent preconditioning? The preconditioner-only analysis does not carry over: with momentum the canonical…
人工智能投资策略的评估
We study the problem of auditing a black-box algorithmic decision-maker from observable inputs and outputs alone. Our main result is an exact decomposition: under precisely characterized conditions, the cumulative \emph{regret} of a dynamic policy equals the sum of per-period covariances between the cost vector and the policy's decision. This extends the single-period identity of Aldridge~(2026) to the full multi-period setting of stochastic dynamic programming. We prove the…
重新审视免带宽推断:样本分割方法
Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the…
可能误设与非平稳模型中异方差和自相关稳健推断的演化谱理论
We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run…
非平稳条件下 HAR 检验的 fixed-b 极限分布与拒绝概率误差
We show that the limiting distribution of HAR test statistics under fixed-b asymptotics is not pivotal when the data are nonstationary (i.e., time-varying autocovariance structure). It takes the form of a complicated function of Gaussian processes and depends on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, fixed-b inference methods based on stationarity are not theoretically valid in…