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Davison与Rodionov对《通过下注估计有界随机变量均值》的讨论AI 解读

We congratulate the authors on a wide-ranging contribution to a statistical hardy perennial. The restriction that the support be known and bounded appears highly restrictive, yet Proposition 3 suggests much wider potential for applications, one of which we briefly explore below. The Pickands–Balkema–de Haan theorem (Balkema & de Haan, 1974; Pickands, 1975) establishes that the distribution of a random variable X, conditioned on its exceeding a high threshold u can in rather…

Howard对《通过下注估计有界随机变量均值》的讨论AI 解读

I congratulate the authors on this creative and well-written contribution. It’s always a delight to see new insights into such a fundamental problem as inference for the mean of bounded observations, and certainly inspires excitement about the future of game-theoretic statistical inference. Besides the impressive technical contributions, I appreciate how the authors draw previously unappreciated connections between work in information theory, finance, and online learning,…

李佳怡、李远通与戴晓武对“通过下注估计有界随机变量均值”的讨论AI 解读

We congratulate Waudby-Smith and Ramdas for their interesting paper Waudby-Smith and Ramdas (2020b) in generating confidence intervals and time-uniform confidence sequences for mean estimation with bounded observations. Their methodology utilises composite non-negative martingales and establishes a connection to game-theoretic probability. Our comments will focus on numerical comparisons with alternative methods. The corresponding code is available at…

王若度对《通过下注估计有界随机变量均值》的讨论AI 解读

I congratulate Ian Waudby-Smith and Aaditya Ramdas for this excellent contribution to the theory of e-testing (or testing by betting). Over the past several years, this theory has been developed rapidly in multiple exciting directions. The contribution of Waudby-Smith and Ramdas is an important piece in this active stream of literature. I have a few comments on the approach in the current paper and its generalisations. The main approach taken in the paper (see its Theorem…

江荣与余克明对《通过下注估计有界随机变量均值》的讨论AI 解读

We want to congratulate the authors on estimating means of bounded random variables in both with- and without-replacement settings. The authors constructed confidence intervals and time-uniform confidence sequences for the mean of a bounded random variable using test supermartingale technique. It deepens our understanding of the confidence sequence. Confidence sequence is one particular tool in sequential design that facilitates anytime-valid inference. In particular,…

超越尖锐零假设的随机化推断：有界零假设与个体处理效应分位数AI 解读

Abstract Randomisation inference (RI) is typically interpreted as testing Fisher’s ‘sharp’ null hypothesis that all unit-level effects are exactly zero. This hypothesis is often criticised as restrictive and implausible, making its rejection scientifically uninteresting. We show, however, that many randomisation tests are also valid for a ‘bounded’ null hypothesis under which the unit-level effects are all non-positive (or all non-negative) but are otherwise heterogeneous.…

基于回归秩得分的异质分位数处理效应去偏推断AI 解读

Abstract Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modelling such heterogeneity. We propose a new method for inference on heterogeneous quantile treatment effects (HQTE) in the presence of high-dimensional covariates. Our estimator combines an ℓ1-penalised regression adjustment with a quantile-specific bias…

随机实验中处理效应的半参数估计AI 解读

Abstract We develop new semi-parametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large, and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semi-parametric models for the outcome distributions. We derive…

StarTrek：控制错误发现率的组合变量选择AI 解读

Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high-dimensional graphical models and control the…

重印：高维分位数回归的假设检验AI 解读

Quantile regression has been an important analytical tool in econometrics since it was proposed in 1970s. Many advantages make it still popular in the era of big data. This paper focuses on the testing problems of high-dimensional quantile regression, supplementing to robust methods in the literature of high-dimensional hypothesis testing. We first construct a new test statistic based on the quantile regression score function. The new test statistic avoids the inverse…

Retire：高维稳健期望分位数回归AI 解读

High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in high-dimensional data. The former is computationally challenging due to the non-smooth nature of the check loss, and the latter is sensitive to heavy-tailed error distributions. In this paper, we propose and study (penalized) robust expectile regression…

具有共同结构的面板多折点分位数回归模型AI 解读

Stimulated by the analysis of a data set on financial portfolio returns, we propose a multi-kink quantile regression (MKQR) model with latent homogeneous structure for panel data analysis. The proposed model accounts for both homogeneity and heterogeneity among individuals and parameters in panel data analysis. From statistical modeling point of view, it well balances the risk of misspecification and the model parsimony. From practical point of view, it is able to reveal not…

基于含噪观测的分布推断AI 解读

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical…

有序响应模型的简便半参数估计AI 解读

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameters, and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite-dimensional parameters in the model, we construct nonparametric maximum likelihood estimates for the error distribution based on the related binary choice data or the…

贝叶斯推断中自适应求积的随机收敛速率及应用AI 解读

We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior density, the coverage probabilities of approximate credible sets, and approximate moments and quantiles, therefore, guaranteeing fast asymptotic convergence of approximate summary statistics used in practice. The family of quadrature rules…

极值估计量的自助法AI 解读

This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimator. For the peaks-over-threshold method, we show the bootstrap consistency of the confidence intervals. By contrast, the asymptotic expansion of the quantile process of the…

重尾密度估计AI 解读

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior…

洛伦兹占优的似然比检验AI 解读

In testing hypotheses pertaining to Lorenz dominance (LD), researchers have examined second- and third-order stochastic dominance using empirical Lorenz processes and integrated stochastic processes with the aid of bootstrap analysis. Among these topics, analysis of third-order stochastic dominance (TSD) based on the notion of risk aversion has been examined using crossing (generalized) Lorenz curves. These facts motivated the present study to characterize distribution pairs…

“风险率”博弈模型的分位数分析AI 解读

This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the ”hazard-rate”). The goal is to use data on players’ actions to recover the distribution of private information. We show that the structural…

潜在指数选择模型中的锐界AI 解读

A fundamental question underlying the literature on partial identification is: what can we learn about parameters that are relevant for policy but not necessarily point-identified by the exogenous variation we observe? This paper provides an answer in terms of sharp, analytic characterizations and bounds for an important class of policy-relevant treatment effects , consisting of marginal treatment effects and linear functionals thereof, in the latent index selection model as…

利用二元工具变量估计服从者预期短缺处理效应AI 解读

Estimating the causal effect of a treatment or exposure for a subpopulation is of great interest in many biomedical and economical studies. Expected shortfall, also referred to as the super-quantile, is an attractive effect-size measure that can accommodate data heterogeneity and aggregate local information of effect over a certain region of interest of the outcome distribution. In this article, we propose the ComplieRExpected Shortfall Treatment Effect (CRESTE) model under…

混杂变量维度增长时利用神经网络推断一般处理效应AI 解读

Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome or treatment to confounders nonparametrically. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using artificial…

基于汇总表数据的免调参非参数密度估计AI 解读

Administrative data are often easier to access as tabulated summaries than in the original format due to confidentiality concerns. Motivated by this practical feature, we propose a novel nonparametric density estimation method from tabulated summary data based on maximum entropy and prove its strong uniform consistency. Unlike existing kernel-based estimators, our estimator is free from tuning parameters and admits a closed-form density that is convenient for post-estimation…

含不可观测异质性的时空模型估计与自助法AI 解读

Proposed herein is a novel spatiotemporal model to characterize the unobserved heterogeneity across individuals using quantile-function-based correlated random effects and heteroscedastic innovations in a general framework. This model can be used to explore the influence of space-specific factors on latent effects at different quantile levels by controlling for spatiotemporal effects. A two-stage estimation procedure is introduced in which (i) the method of moments is used…