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Summary We propose a new double-order selection test for checking second-order stationarity of a time series. To develop the test, a sequence of systematic samples is defined via Walsh functions. Then the deviations of the autocovariances based on these systematic samples from the corresponding autocovariances of the whole time series are calculated and the uniform asymptotic joint normality of these deviations over different systematic samples is obtained. With a…

Group Bound：不对设计矩阵作假设的稀疏高维回归变量组置信区间AI 解读

Summary It is in general challenging to provide confidence intervals for individual variables in high dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a ‘group bound’ confidence interval can be derived without making any assumptions on the design matrix. The lower bound for the regression coefficient of individual variables can be derived via linear programming. The idea also generalizes naturally to groups of…

行列式点过程模型与统计推断AI 解读

Summary Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric…

通过旋转使 Fisher 线性判别稀疏化AI 解读

Summary Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis. To use them efficiently, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the sparsity needed. We propose a family of rotations to create the sparsity required. The basic idea is to use the principal components of the sample…

稀疏异步纵向数据的回归分析AI 解读

Summary We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or…

具有收敛保证的高维偏相关估计凸伪似然框架AI 解读

Summary Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l 1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear…

部分观测函数型数据的主成分分析与补全AI 解读

Summary Functional data are traditionally assumed to be observed on the same domain. Motivated by a data set of heart rate temporal profiles, we develop methodology for the analysis of incomplete functional samples where each curve may be observed on a subset of the domain and unobserved elsewhere. We formalize this observation regime and develop the fundamental procedures of functional data analysis for this framework: estimation of parameters (mean and covariance operator)…

两水平析因设计的潜在结果因果推断AI 解读

Summary A framework for causal inference from two-level factorial designs is proposed, which uses potential outcomes to define causal effects. The paper explores the effect of non-additivity of unit level treatment effects on Neyman's repeated sampling approach for estimation of causal effects and on Fisher's randomization tests on sharp null hypotheses in these designs. The framework allows for statistical inference from a finite population, permits definition and…

序贯准蒙特卡洛AI 解读

Summary We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is O{Nlog(N)}, where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate OP(N−1/2). The only requirement to implement SQMC algorithms is the…

随机图模型中的局部依赖：刻画、性质与统计推断AI 解读

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing…

空间点过程的拟似然AI 解读

Summary Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering that is not accounted for by the available covariates, likelihoodbased inference becomes computationally cumbersome owing to the complicated nature of the…

基于内在自回归的空间混合线性模型 h-似然方法AI 解读

Summary We consider sparse spatial mixed linear models, particularly those described by Besag and Higdon, and develop an h-likelihood method for their statistical inference. The method proposed allows for singular precision matrices, as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model. Furthermore, we generalize…

多水平干预与多分量中介下的因果中介分析AI 解读

Summary Mediation analysis is an important tool in social and medical sciences as it helps to understand why an intervention works. The commonly used approach, given by Baron and Kenny, requires the strong assumption ‘sequential ignorability’ to yield causal interpretation. Ten Have and his colleagues proposed a rank preserving model to relax this assumption. However, the rank preserving model is restricted to the case with binary intervention and single mediator and needs…

通过稀疏化二元分割检测高维时间序列的多个变点AI 解读

Summary Time series segmentation, which is also known as multiple-change-point detection, is a well-established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second-order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms…

动态函数主成分AI 解读

Summary We address the problem of dimension reduction for time series of functional data (Xt:t∈Z). Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each X t represents one intraday curve. We argue that functional principal component analysis, though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time…

Summary We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates V when randomization of the instrument is only true conditionally on a high dimensional vector of…

规则格点上的稀疏加性回归AI 解读

Summary We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate optimal estimator which is adaptive to the unknown sparsity and smoothness of the response function. The estimator is derived within a Bayesian formalism but can be naturally viewed as a penalized maximum likelihood estimator with the complexity penalties on the…

有无不等式约束的非平稳时间序列回归推断AI 解读

Summary We consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non-stationary behaviours over time. Meanwhile, the regression parameters may be subject to linear inequality constraints. A simple and unified procedure for structural stability checks and parameter inference is proposed. In the case where the regression parameters are constrained, the methodology proposed…

完全依从或完全不依从生存研究中的因果推断：半参数变换模型AI 解读

Summary We consider causal inference in randomized survival studies with right-censored outcomes and all-or-nothing compliance, using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups, conditionally on covariates and latent compliance type. Estimands depending on these distributions, e.g. the complier average causal effect, the complier effect on survival beyond time t and the complier quantile effect, are…

边际期望损失的估计：当相关变量处于极端值时AI 解读

Summary Denote the loss return on the equity of a financial institution as X and that of the entire market as Y. For a given very small value of p > 0, the marginal expected shortfall (MES) is defined as E{X|Y>QY(1−p)}, where Q Y(1 − p) is the (1 − p)th quantile of the distribution of Y. The MES is an important factor when measuring the systemic risk of financial institutions. For a wide non-parametric class of bivariate distributions, we construct an estimator of the MES…

一般因子设计中的渐近置换检验AI 解读

Summary In general factorial designs where no homoscedasticity or a particular error distribution is assumed, the well-known Wald-type statistic is a simple asymptotically valid procedure. However, it is well known that it suffers from a poor finite sample approximation since the convergence to its χ 2 limit distribution is quite slow. This becomes even worse with an increasing number of factor levels. The aim of the paper is to improve the small sample behaviour of the…

联合观测与干预数据估计有向无环图的干预马尔可夫等价类AI 解读

Summary In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modelling of such different data types, based on global parameters consisting of a directed acyclic graph and corresponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the…

Hüsler–Reiss分布与Brown–Resnick过程的估计AI 解读

Summary Estimation of extreme value parameters from observations in the max-domain of attraction of a multivariate max-stable distribution commonly uses aggregated data such as block maxima. Multivariate peaks-over-threshold methods, in contrast, exploit additional information from the non-aggregated ‘large’ observations. We introduce an approach based on peaks over thresholds that provides several new estimators for processes η in the max-domain of attraction of the…

条件推断模型：汇集信息以进行无先验概率推断AI 解读

Summary The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher dimension than the parameter. Here we show that features of the auxiliary variable are often fully observed and, in such cases, a simultaneous dimension reduction and information aggregation can be achieved by conditioning. This…