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利用耦合构造无偏马尔可夫链蒙特卡洛方法AI 解读

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We…

空间数据密度估计的带宽选择AI 解读

Summary Bandwidth choice is crucial in spatial kernel estimation in exploring non-Gaussian complex spatial data. The paper investigates the choice of adaptive and non-adaptive bandwidths for density estimation given data on a spatial lattice. An adaptive bandwidth depends on local data and hence adaptively conforms with local features of the spatial data. We propose a spatial cross-validation (SCV) choice of a global bandwidth. This is done first with a pilot density…

利用稀疏线性规划优化两阶段自适应富集随机试验设计AI 解读

Summary Adaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. The goal is to learn which populations benefit from an experimental treatment. Two critical components of adaptive enrichment designs are the decision rule for modifying…

通过稳健梯度估计实现稳健估计AI 解读

Summary We provide a new computationally efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models, under varied robustness settings, including in the classical Huber ε-contamination model, and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk…

随机干预的因果中介分析AI 解读

Summary Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. We present an analogous decomposition of the population intervention effect, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be…

日内与隔夜波动率的耦合成分 DCS-EGARCH 模型AI 解读

We propose a semi-parametric coupled component exponential GARCH model for intraday and overnight returns that allows the two series to have different dynamical properties. We adopt a dynamic conditional score model with t-distributed innovations that captures the very heavy tails of overnight returns. We propose a several-step estimation procedure that captures the nonparametric slowly moving components by kernel estimation and the dynamic parameters by maximum likelihood.…

混合频率与混合样本数据的协整向量频域估计AI 解读

This paper proposes a simple method for exploiting the information contained in mixed frequency and mixed sample data in the estimation of cointegrating vectors. The asymptotic properties of easy-to-compute spectral regression estimators of the cointegrating vectors are derived and these estimators are shown to belong to the class of optimal cointegration estimators. Furthermore, Wald statistics based on these estimators have asymptotic chi-square distributions which enable…

不可微函数的后验分布AI 解读

This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(θ), where θ is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator θ̂n, its bootstrap approximation, and the Bayesian posterior for θ all agree asymptotically.

结构突变模型中的相关参数变化AI 解读

Structural break time series models, which are commonly used in macroeconomics and finance, capture unknown structural changes by allowing for abrupt changes to model parameters. However, many specifications suffer from an over-parametrization issue, since typically all parameters have to change when a break occurs. We introduce a sparse change-point model to detect which parameters change over time. We propose a shrinkage prior distribution, which controls model parsimony…

高维工具变量回归的统计推断AI 解读

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a…

训练标签不完美时的分类AI 解读

Summary We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector and the true label, we bound the excess risk of an arbitrary classifier trained with imperfect labels in terms of its excess risk for predicting a noisy label. This reveals conditions under which a classifier trained with…

半参数截断模型下基于横截面数据的估计AI 解读

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their…

通过边抽样进行网络交叉验证AI 解读

Summary While many statistical models and methods are now available for network analysis, resampling of network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but it is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. In this paper we propose a new network resampling strategy, based on splitting node pairs…

用于离散参数与不连续似然的非连续哈密顿蒙特卡洛AI 解读

Summary Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters through the embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding…

本质直方图AI 解读

Summary The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the…

放宽容差并作事后校正的近似贝叶斯计算马尔可夫链蒙特卡洛AI 解读

Summary Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure…

基于密度幂散度的稳健经验贝叶斯小区域估计AI 解读

Summary A two-stage normal hierarchical model called the Fay–Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean…

边际似然与交叉验证的关系AI 解读

Summary In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through $k$-fold partitioning or leave-$p$-out subsampling. We show that the marginal likelihood is formally equivalent to exhaustive leave-$p$-out crossvalidation averaged over all values of $p$…

高维 Hotelling T² 检验的自适应推广AI 解读

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling’s $T^{2}$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the…

局部最近邻分类及其半监督学习应用AI 解读

We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution to the excess risk comes from the decision boundary of the optimal Bayes classifier, but we also show that if these conditions are not satisfied, then the dominant contribution may arise from the tails of the marginal distribution of the…

We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression operators as a special case. We show the optimality of our reconstruction operator and demonstrate that the usually considered regression operators generally cannot be optimal reconstruction operators. Our estimation theory allows for…

通过乘子自助法进行稳健推断AI 解读

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression,…

变点模型的分割与估计：假阳性控制和置信区域AI 解读

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to…

稀疏矩阵检测的统计与计算极限AI 解读

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and columns are individually $k$-sparse. We provide a tight characterization of the statistical and computational limits for sparse matrix detection, which precisely describe when achieving optimal detection is easy, hard or impossible,…