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凸性约束模型中局部参数的统计推断AI 解读

In this article, we develop automated inference methods for “local” parameters in a collection of convexity constrained models based on the natural constrained tuning-free estimators. A canonical example is given by the univariate convex regression model, in which automated inference is drawn for the function value, the function derivative at a fixed interior point, and the anti-mode of the convex regression function, based on the widely used tuning-free, piecewise linear…

多维保序回归及其他单调模型的置信区间AI 解读

We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, Han and Zhang (2020) obtained a pointwise limit distribution theory for the so-called block max–min and min–max estimators (Fokianos, Leucht and Neumann (2020); Deng and Zhang (2020)) in this model, but inference remains a difficult problem due to the nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the…

多维空间与图上的保序回归AI 解读

In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^{d}$ with ${d\ge2}$ and $N(0,1)$ noise, the minimax rate for the $\ell_{2}$ risk is known to be bounded from below by $n^{-1/d}$ when the unknown mean function $f$ is nondecreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor $(\log n)^{\gamma}$…

超越高斯近似：独立随机向量之和最大值的自助法AI 解读

The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on an ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous…