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函数型数据的极端深度及其应用AI 解读

We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous…

基于 SURE 的双重收缩估计AI 解读

The article is concerned with empirical Bayes shrinkage estimators for the heteroscedastic hierarchical normal model using Stein's unbiased estimate of risk (SURE). Recently, Xie, Kou, and Brown proposed a class of estimators for this type of problems and established their asymptotic optimality properties under the assumption of known but unequal variances. In this article, we consider this problem with unequal and unknown variances, which may be more appropriate in real…

预测变量对函数型响应影响的检验AI 解读

This article examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost surely zero or not, without imposing any model relating response and covariate. The covariate could be univariate, multivariate, or functional. Our test statistic is a quadratic form involving univariate nearest neighbor smoothing and the…

短程与长程依赖下单调函数的推断：置信区间与新的普适极限AI 解读

We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which previous methods are forced to deal with. The resulting…

用局部近似加速计算密集模型的渐近精确 MCMCAI 解读

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into…

在整群随机设计中使用排序集抽样改进处理效应推断AI 解读

Xinlei Wanga, Johan Limb & Lynne Stokesa*a Department of Statistical Science, Southern Methodist University, Dallas, TX, USAb Seoul National University, Seoul, KoreaCONTACT Lynne Stokes slstokes@smu.edu Department of Statistical Science, Southern Methodist University, Dallas, TX 75275-0332.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to…

通过自动稀疏旋转实现快速贝叶斯因子分析AI 解读

Rotational post hoc transformations have traditionally played a key role in enhancing the interpretability of factor analysis. Regularization methods also serve to achieve this goal by prioritizing sparse loading matrices. In this work, we bridge these two paradigms with a unifying Bayesian framework. Our approach deploys intermediate factor rotations throughout the learning process, greatly enhancing the effectiveness of sparsity inducing priors. These automatic rotations…

非可忽略缺失下正态及正态混合模型的可识别性AI 解读

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form,…

An ongoing challenge in the analysis of document collections is how to summarize content in terms of a set of inferred themes that can be interpreted substantively in terms of topics. The current practice of parameterizing the themes in terms of most frequent words limits interpretability by ignoring the differential use of words across topics. Here, we show that words that are both frequent and exclusive to a theme are more effective at characterizing topical content, and…

Peter Hall 对非参数函数估计与建模的贡献AI 解读

Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape…

Peter Hall 对自助法的贡献AI 解读

Professor Peter Hall's first publication appeared in 1977, one year after he was awarded DPhil from the University of Oxford and MSc from the Australian National University (ANU).His first paper on the bootstrap appeared in 1985[Hall (1985))] on the block bootstrap of spatial point patterns, six years after the seminal paper [Efron (1979)] that introduced the bootstrap method.Hall (1985) was his 103rd publication and proposed resampling "tiles" of spatial data ("coverage…

Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling…

非参数协变量调整回归AI 解读

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied…

第一投影方向的渐近理论AI 解读

For a response variable $Y$, and a $d$ dimensional vector of covariates $\mathbf{X}$, the first projective direction, $\mathbf{\vartheta}$, is defined as the direction that accounts for the most variability in $Y$. The asymptotic distribution of an estimator of a trimmed version of $\mathbf{\vartheta}$ has been characterized only under the assumption of the single index model (SIM). This paper proposes the use of a flexible trimming function in the objective function, which…

全基因组关联研究中高维误设混合模型的分析AI 解读

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent genome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random…

局部内蕴平稳性及其统计推断AI 解读

Dense spatial data are commonplace nowadays, and they provide the impetus for addressing nonstationarity in a general way. This paper extends the notion of intrinsic random function by allowing the stationary component of the covariance to vary with spatial location. A nonparametric estimation procedure based on gridded data is introduced for the case where the covariance function is regularly varying at any location. An asymptotic theory is developed for the procedure on a…

纵向与聚类数据半变系数模型的有效估计AI 解读

In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are…

Harris 常返马尔可夫链下非线性回归的估计AI 解读

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov…

学生化两样本 U 统计量的 Cramér 型中等偏差及应用AI 解读

Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramér-type moderate deviation theorems for Studentized two-sample $U$-statistics in a general framework, including the two-sample $t$-statistic and Studentized Mann–Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is…

数字实验中异质性处理效应的非参数贝叶斯分析AI 解读

Randomized controlled trials play an important role in how Internet companies predict the impact of policy decisions and product changes. In these “digital experiments,” different units (people, devices, products) respond differently to the treatment. This article presents a fast and scalable Bayesian nonparametric analysis of such heterogenous treatment effects and their measurement in relation to observable covariates. New results and algorithms are provided for…

含大量控制变量的广义线性模型选择后推断AI 解读

This article considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunizes against model selection mistakes and apply it to the case of logistic binary choice model. More specifically we propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α0, a parameter in front of the regressor…

波动率风险溢价如何反映流动性供给与尾部风险对冲需求？AI 解读

This article provides a data-driven analysis of the volatility risk premium, using tools from high-frequency finance and Big Data analytics. We argue that the volatility risk premium, loosely defined as the difference between realized and implied volatility, can best be understood when viewed as a systematically priced bias. We first use ultra-high-frequency transaction data on SPDRs and a novel approach for estimating integrated volatility on the frequency domain to compute…

高维面板模型中的推断：枪支管制应用AI 解读

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high-dimensional setting. The setting allows the number of time-varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time-varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the…

因子增广向量自回归模型的估计与推断AI 解读

The factor-augmented vector autoregressive (FAVAR) model is now widely used in macroeconomics and finance. In this model, observable and unobservable factors jointly follow a vector autoregressive process, which further drives the comovement of a large number of observable variables. We study the identification restrictions for FAVAR models, and propose a likelihood-based two-step method to estimate the model. The estimation explicitly accounts for factors being partially…