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高维数据点间距离的渐近正态性及其两样本检验应用AI 解读

Interpoint distances have applications in many areas of probability and statistics. Thanks to their simplicity of computation, interpoint distance-based procedures are particularly appealing for analysing small samples of high-dimensional data. In this paper, we first study the asymptotic distribution of interpoint distances in the high-dimension, low-sample-size setting and show that it is normal under regularity conditions. We then construct a powerful test for the…

评估两项多特征研究中发现的可重复性AI 解读

Replicability analysis aims to identify the overlapping signals across independent studies that examine the same features. For this purpose we develop hypothesis testing procedures that first select the promising features from each of two studies separately. Only those features selected in both studies are then tested. The proposed procedures have theoretical guarantees regarding their control of the familywise error rate or false discovery rate on the replicability claims.…

近似贝叶斯计算的渐近性质AI 解读

Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates…

随机设计与未知相关结构下的相关误差局部多项式回归AI 解读

Automated or data-driven bandwidth selection methods tend to break down in the presence of correlated errors. While this problem has previously been studied in the fixed design setting for kernel regression, the results were applicable only when there is knowledge about the correlation structure. This article generalizes these results to the random design setting and addresses the problem in situations where no prior knowledge about the correlation structure is available. We…

贝叶斯空间单调多元回归AI 解读

We consider monotonic, multiple regression for contiguous regions. The regression functions vary regionally and may exhibit spatial structure. We develop Bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump Markov chain Monte Carlo techniques. Spatial dependence is incorporated by a flexible prior distribution which is tuned using crossvalidation and Bayesian…

Akaike 信息准则的渐近选择后推断AI 解读

Ignoring the model selection step in inference after selection is harmful. In this paper we study the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the candidate set of models. We exploit the overselection property of this criterion in constructing a selection region, and we obtain the asymptotic distribution of estimators and linear…

纵向网络随机区块模型的半参数扩展AI 解读

We propose an extension of the stochastic block model for recurrent interaction events in continuous time, where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. We show that the model is identifiable and estimate it with a semiparametric variational expectation-maximization algorithm. We develop two versions of the method, one using…

精度矩阵估计量特征的收缩AI 解读

We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an |$L_1$| penalty on a linear or affine function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and propose an alternating direction method of multipliers algorithm for…

线性模型中的贝叶斯因子AI 解读

We show that the Bayes factor for testing whether a subset of coefficients are zero in the normal linear regression model gives the uniformly most powerful test amongst the class of invariant tests discussed in Lehmann & Romano (2005) if the prior distributions for the regression coefficients are in a specific class of distributions. The priors in this class can have any elliptical distribution, with a specific scale matrix, for the subset of coefficients that are being…

事件时间结局下最优个体化治疗规则的目标学习集成AI 解读

We consider estimation of an optimal individualized treatment rule when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying the expected time to occurrence of an event of interest. We use semiparametric efficiency theory to construct estimators with properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at directly estimating the…

消除协变量关联的权重：因果效应估计的统一加权框架AI 解读

Weighting methods offer an approach to estimating causal treatment effects in observational studies. However, if weights are estimated by maximum likelihood, misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance. In this paper, we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting. We derive conditions…

分量分别删失的复合终点半参数回归分析AI 解读

Composite endpoints with censored data are commonly used as study outcomes in clinical trials. For example, progression-free survival is a widely used composite endpoint, with disease progression and death as the two components. Progression-free survival time is often defined as the time from randomization to the earlier occurrence of disease progression or death from any cause. The censoring times of the two components could be different for patients not experiencing the…

条件自回归与内蕴自回归的边界修正AI 解读

This paper discusses edge correction for a large class of conditional and intrinsic autoregressions on two-dimensional finite regular arrays. The proposed method includes a novel reparameterization, retains the simple neighbourhood structure, ensures the nonnegative definiteness of the precision matrix, and enables scalable matrix-free statistical computation. The edge correction provides new insight into how higher-order differencing enters into the precision matrix of a…

《惩罚样条估计量的渐近性质》勘误AI 解读

Biometrika (2009) 96, pp. 529–44. In Lemmas A1 and A2, Theorem 2, and the line before equation (17), |$K_q\ge 1$| should be replaced by |$K_q\in[1,\infty)$|⁠, since |$K_q$| needs to be bounded. In Assumption 1, |$\delta=o(K^{-1})$| should read |$\max_{1\le j\le K}|\kappa_{j+1}-2\kappa_j+\kappa_{j-1}|=o(K^{-1})$|⁠. At the typesetting stage an error occurred while adding parentheses; throughout the paper it should be |$n^{1/(2q)-1}\lambda^{-1/(2q)}$| instead of |$n^{1/(2q-1)}\lambda^{-1/(2q)}$…

连续空间总体的基于抽样设计制图AI 解读

We analyse the estimation of values of a survey variable throughout a continuum of points in a study area when a sample of points is selected by a probabilistic sampling scheme. At each point, the value is estimated using an inverse distance weighting interpolator, and maps of the survey variable can be obtained. We investigate the design-based asymptotic properties of the interpolator when the study area remains fixed and the number of sampled points approaches infinity,…

具有恒定覆盖率的自适应多组置信区间AI 解读

Commonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average, but their actual coverage rate for a given group will be above or below the nominal rate, depending on the group mean. While correct coverage for a given group can be achieved with a standard |$t$|-interval, this approach is not adaptive to the available information about the distribution of group-specific means. In this article we construct…

高维协方差与精度矩阵的稳健估计AI 解读

High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a…

高维情形下主成分数量的选择AI 解读

We consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The…

记录链接中微聚类的理论极限AI 解读

There has been substantial recent interest in record linkage, where one attempts to group the records pertaining to the same entities from one or more large databases that lack unique identifiers. This can be viewed as a type of microclustering, with few observations per cluster and a very large number of clusters. We show that the problem is fundamentally hard from a theoretical perspective and, even in idealized cases, accurate entity resolution is effectively impossible…

按估计倾向得分修剪的观察性研究中因果效应的渐近推断AI 解读

Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores close to |$0$| or |$1$|⁠, so both practical and theoretical researchers suggest dropping units with extreme estimated propensity scores. However, existing trimming methods often do not incorporate the uncertainty in this design stage and…

含噪高频数据中误差分布的频域分析AI 解读

Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Itô diffusion process, we propose to estimate the measurement error density function by applying a deconvolution technique with appropriate localization. Our estimator, which does not require equally-spaced…

波动率泛函的局部非参数 bootstrapAI 解读

Volatility functionals are widely used in financial econometrics. In the literature, they are estimated with realized volatility functionals using high-frequency data. In this paper we introduce a nonparametric local bootstrap method that resamples the high-frequency returns with replacement in local windows shrinking to zero. While the block bootstrap in time series (Hall et al., 1995) aims to reduce correlation, the local bootstrap is intended to eliminate the…

不可忽略无应答下多元缺失数据分析的最优伪似然估计AI 解读

Tang et al. (2003) considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the…

多臂多阶段临床试验中的一致最小方差条件无偏估计AI 解读

Multi-arm multi-stage clinical trials compare several experimental treatments with a control treatment, with poorly performing treatments dropped at interim analyses. This leads to inferential challenges, including the construction of unbiased treatment effect estimators. A number of estimators which are unbiased conditional on treatment selection have been proposed, but are specific to certain selection rules, may ignore the comparison to the control and are not all minimum…