论文检索

通过双尺度方法改进同方差非参数随机设计回归的方差估计AI 解读

We study estimation of a constant conditional variance $σ^2$ in nonparametric regression with a $d$-dimensional random design. This is an important problem, and similar questions arise in causal inference. The regression function is $β_b$-Hölder smooth, the design density is $β_g$-Hölder smooth and bounded above and away from zero, and we consider the nonparametric regime $β_b>1$ and $d>4β_b$. Set $β_g^\star=β_b(1-4β_b/d)/\{1+2β_b/d+8(β_b/d)^2\}$. We give an estimator whose…

随机实验的锐极小极大理论AI 解读

We study minimax-optimal designs and estimators for estimating the sample average treatment effect in finite population randomized experiments, where both design and estimator are unrestricted. For binary potential outcomes, we show this minimax risk is equivalent to the minimax risk $ρ_n^*$ of an estimation problem with $2$ unknown parameters. We leverage this reduction to establish a second-order risk expansion $ρ_n^* = n^{-1} - Cn^{-4/3} + o_n(n^{-4/3})$ for an explicit…

包含算法随机性的两阶段观测模型统计推断AI 解读

Randomized algorithms, such as random sampling, random projections, and stochastic optimization, are increasingly used to reduce the computational cost of modern statistical analysis. These algorithms introduce algorithmic randomness in addition to the sampling randomness in the data, and this extra source of variation complicates statistical inference. We develop a framework for valid inference in such two-stage observation models, where data are first generated from an…

相关双侧高斯检验中 BH 程序可能无法控制错误发现率AI 解读

We show that the Benjamini--Hochberg procedure can fail to control the false discovery rate (FDR) at its nominal level for correlated two-sided Gaussian $p$-values. We construct a factor model for which, at level $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR>0.0104$ for all sufficiently large numbers of hypotheses. This disproves a conjecture widely believed to be true for twenty years. Monte Carlo experiments are consistent with the theoretical result.…

在控制错误发现率下识别分布差异AI 解读

We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p-values and…

双重稳健的近端合成控制AI 解读

To infer the treatment effect for a single treated unit using panel data, synthetic control methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing synthetic control methods rely on correctly…

稀疏回归的正则性条件AI 解读

Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue, compatibility, and $\ell_q$ sensitivity properties. However, some of the central aspects of these conditions are not well understood. For instance, it is unknown if these conditions can be checked efficiently on any given data set. This is…

预测的高维渐近理论：岭回归与分类AI 解读

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to γ\in (0, \, \infty)$, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance…