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高维线性回归逐协变量多重检验变量选择法的狭义复现AI 解读

Summary Chudik, Kapetanios, & Pesaran (Econometrica 2018, 86, 1479‐1512) propose a one covariate at a time, multiple testing (OCMT) approach to variable selection in high‐dimensional linear regression models as an alternative approach to penalised regression. We offer a narrow replication of their key OCMT results based on the Stata software instead of the original MATLAB routines. Using the new user‐written Stata commands baing and ocmt , we find results that match closely…

预测目标未知时如何解释点预测AI 解读

Abstract Point forecasts can be interpreted as functionals (i.e., point summaries) of predictive distributions. We extend methodology for the identification of the functional based on time series of point forecasts and associated realizations. Focusing on state‐dependent quantiles and expectiles, we provide a generalized method of moments estimator for the functional, along with tests of optimality under general joint hypotheses of functional relationships and information…

投入市场摩擦下的生产函数估计AI 解读

Abstract Behind many production function estimators lies a crucial assumption that the firm's choice of intermediate inputs depends only on observed choices of other inputs and on unobserved productivity. This assumption fails when market frictions distort the firm's input choices. I derive a test for the assumption, which is rejected in several industries. Using weak identification asymptotics, I show that when the assumption fails, a simplified dynamic panel estimator can…

通过降维构建简约的个性化剂量探索模型AI 解读

Summary Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To tackle this problem, we propose a dimension reduction framework that effectively reduces the estimation to an optimization on a lower-dimensional subspace of the covariates. We exploit the fact that the individualized dose rule can be…

存在中间混杂变量时的非参数有效因果中介分析AI 解读

Summary Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two…

用于快速推断的自适应计算机实验复合网格设计AI 解读

Summary Experiments are often used to produce emulators of deterministic computer code. This article introduces composite grid experimental designs and a sequential method for building the designs for accurate emulation. Computational methods are developed that enable fast and exact Gaussian process inference even with large sample sizes. We demonstrate that the proposed approach can produce emulators that are orders of magnitude more accurate than current approximations at…

刀切经验似然：小带宽、稀疏网络与高维渐近AI 解读

Summary This article aims to shed light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of the jackknife empirical likelihood. Examples include small-bandwidth asymptotics for semiparametric inference and goodness-of-fit testing, sparse-network asymptotics, many-covariates asymptotics for regression models, and many-weak-instruments asymptotics for instrumental variable regression. We first establish…

利用 ROC 曲线评估生存数据中的治愈状态预测AI 解读

Summary Survival analysis relies on the hypothesis that, if the follow-up is long enough, the event of interest will eventually be observed for all observations. This assumption, however, is often not realistic. The survival data then contain a cure fraction. A common approach to modelling and analysing this type of data consists in using cure models. Two types of information can therefore be obtained: the survival at a given time and the cure status, both possibly modelled…

Wilks 现象的相变AI 解读

Summary Wilks’ theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the conventional Wilks’ phenomenon of the likelihood ratio test statistic often fails. Although new approximations have been proposed in high-dimensional settings, there still lacks a clear statistical guideline regarding how to choose…

依赖数据样本分位数的块自助法最优性与经验选块AI 解读

Summary We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the sub- sampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample size to block length. The hybrid block bootstrap is shown to give…

Stein 正态近似方法：回忆与思考AI 解读

This paper is a short exposition of Stein’s method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it provides glimpses into the many approaches to constructing Stein identities and the diverse applications of Stein’s method to mathematical problems. It also includes anecdotes of historical interest, including how Stein discovered his method…

查尔斯·斯坦与不变性：从 Hunt–Stein 定理谈起AI 解读

When statistical decision theory was emerging as a promising new paradigm, Charles Stein was to play a major role in the development of minimax theory for invariant statistical problems. In some of his earliest work with Gil Hunt, he set out to prove that, in problems where invariant procedures have constant risk, any best invariant test would be minimax among all tests. Although finding it not quite true in general, this led to the legendary Hunt–Stein theorem, which…

We revisit a paper by Charles Stein, and discuss its follow-up.

时间序列中变点的最优估计AI 解读

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real…

何谓分辨率：超分辨显微成像的统计极小极大检验视角AI 解读

As a general rule of thumb the resolution of a light microscope (i.e., the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)—the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well-known Abbe and Rayleigh criteria, dating back to the end of the 19th century. However, during the last…

分布序列变点的在线监测AI 解读

We propose a method for the detection of a change point in a sequence {Fi} of distributions, which are available through a large number of observations at each i≥1. Under the null hypothesis, the distributions Fi are equal. Under the alternative hypothesis, there is a change point i∗>1, such that Fi=G for i≥i∗ and some unknown distribution G, which is not equal to F1. The change point, if it exists, is unknown, and the distributions before and after the potential change…

极小极大最优的条件独立性检验AI 解读

We consider the problem of conditional independence testing of X and Y given Z where X,Y and Z are three real random variables and Z is continuous. We focus on two main cases—when X and Y are both discrete, and when X and Y are both continuous. In view of recent results on conditional independence testing [Ann. Statist. 48 (2020) 1514–1538], one cannot hope to design nontrivial tests, which control the type I error for all absolutely continuous conditionally independent…

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…

波动率估计的耦合理论AI 解读

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting.…

二阶 Stein 公式：SURE 的风险估计及高维推断应用AI 解读

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf is the divergence of the function f and z is a standard normal vector. This paper aims to propose a second-order Stein formula to characterize the variance of such random variables for all functions f(z) with square integrable gradient, and to demonstrate the usefulness of this second-order Stein formula in various applications. In…

摘要暂缺

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in various fields. While the exchangeability assumption is sensible in many cases, it implies that the size of the clusters necessarily grows linearly with the sample size, and such feature may be undesirable for some applications. We present here a flexible class of…

具有两个有界矩的分布下的稳健 k-means 聚类AI 解读

We consider the robust algorithms for the k-means clustering problem where a quantizer is constructed based on N independent observations. Our main results are median of means based nonasymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of (Ann. Statist. 9 (1981) 135–140) who showed that the existence of two moments is sufficient for…

两样本汇总数据孟德尔随机化中的去偏逆方差加权估计AI 解读

Mendelian randomization (MR) has become a popular approach to study the effect of a modifiable exposure on an outcome by using genetic variants as instrumental variables. A challenge in MR is that each genetic variant explains a relatively small proportion of variance in the exposure and there are many such variants, a setting known as many weak instruments. To this end, we provide a theoretical characterization of the statistical properties of two popular estimators in MR:…