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利用高阶结构进行网络社区检测AI 解读

Summary In many real-world networks, it is often observed that subgraphs or higher-order structures of certain configurations, e.g., triangles and by-fans, are overly abundant compared to standard randomly generated networks (Milo et al., 2002). However, statistical models accounting for this phenomenon are limited, especially when community structure is of interest. This limitation is coupled with a lack of community detection methods that leverage subgraphs or higher-order…

控制错误覆盖声明率的选择性保形推断AI 解读

SUMMARY Conformal inference is a popular tool for constructing prediction intervals. We consider here the scenario of post-selection/selective conformal inference, that is, prediction intervals are reported only for individuals selected from unlabelled test data. To account for multiplicity, we develop a general split conformal framework to construct selective prediction intervals with the false coverage-statement rate control. We first investigate the false coverage…

混合样本检测的现状数据回归分析AI 解读

Summary Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening for infectious diseases. Benefits are realized through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested…

交叉验证中渐近最优带宽的显式解AI 解读

Abstract We show that least-squares cross-validation methods share a common structure that has an explicit asymptotic solution, when the chosen kernel is asymptotically separable in bandwidth and data. For density estimation with a multivariate Student-t(ν) kernel, the cross-validation criterion becomes asymptotically equivalent to a polynomial of only three terms. Our bandwidth formulae are simple and noniterative, thus leading to very fast computations, their integrated…

协变量诱导的依赖左截断下的双重稳健估计AI 解读

Summary In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. For estimation of the distribution of the time to event, conventional methods adjusting for left truncation tend to rely on the quasi-independence assumption that the truncation time and the event time are independent on the observed region. This assumption is violated when there is dependence between the truncation time and the event time,…

Chatterjee 秩相关的自助法失效问题AI 解读

Abstract While researchers commonly use the bootstrap to quantify the uncertainty of an estimator, it has been noticed that the standard bootstrap, in general, does not work for Chatterjee’s rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee’s rank correlation thus falls into a category of statistics that are asymptotically normal, but…

时间平均方差常数的渐近恒定风险估计量AI 解读

Summary Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top…

Toeplitz 协方差矩阵的高效非参数估计AI 解读

Abstract A new efficient nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal…

面对相关或异方差响应时实验设计的极小极大稳健性札记AI 解读

Abstract We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular, it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of…

局部网络统计量的中心极限定理AI 解读

Summary Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making existing approaches unable to describe vertex-specific characteristics. In contrast, rooted subgraphs focus on vertex neighbourhoods, and are fundamental descriptors of local network properties. We derive the…

中心量族推断：针对一族分布中心的假设检验AI 解读

Summary Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null.…

区间删失多状态数据半参数回归模型的最大似然估计AI 解读

Summary Interval-censored multistate data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under…

广义线性混合模型渐近理论的第二项改进AI 解读

Abstract A recent article by Jiang et al. (2022) on generalized linear mixed model asymptotics derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If m denotes the number of groups and n is the average within-group sample size then the asymptotic variances have orders m−1 and (mn)−1, depending on the parameter. We extend this theory to provide explicit forms of the (mn)−1 second terms of the asymptotically harder-to-estimate…

高维投影独立性检验：难题与改进AI 解读

Summary Testing independence between high-dimensional random vectors is fundamentally different from testing independence between univariate random variables. Taking the projection correlation as an example, it suffers from at least three problems. First, it has a high computational complexity of O{n3(p+q)}, where n, p and q are the sample size and dimensions of the random vectors; this limits its usefulness substantially when n is extremely large. Second, the asymptotic…

广义核两样本检验AI 解读

Summary Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do not work well for some scenarios when the dimension of the data is moderate to high due to the curse of dimensionality. We propose a new test statistic that makes use of a common pattern under moderate and high dimensions and…

对象值时间序列的序列独立性检验AI 解读

Summary We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a…

得分驱动模型的最优性AI 解读

Summary Score-driven models have recently been introduced as a general framework to specify time-varying parameters of conditional densities. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback–Leibler divergence between the true conditional…

选择条件工具变量集合的图形工具AI 解读

Summary We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least-squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent…

分离数据下高维 Logistic 回归模型的推断AI 解读

Summary Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the…

支持全范围信息借用的非参数先验AI 解读

Summary Modelling of the dependence structure across heterogeneous data is crucial for Bayesian inference, since it directly impacts the borrowing of information. Despite extensive advances over the past two decades, most available methods only allow for nonnegative correlations. We derive a new class of dependent nonparametric priors that can induce correlations of any sign, thus introducing a new and more flexible idea of borrowing of information. This is achieved thanks…

平行结局的潜力AI 解读

Summary A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that leverages information in multiple outcomes to deal with unmeasured confounding. An important assumption in our approach is conditional independence among multiple outcomes. In contrast to existing proposals in the literature, the roles of…

多重检验与选择性推断中的选择和条件化AI 解读

Summary We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven collection of hypotheses is chosen from some large universe of hypotheses. Subsequently, inference takes place within this data-driven collection, conditioned on the information that was used for the selection. Examples of such methods include basic data splitting as well as modern data-carving methods and…

Page 之后七十年：累积和序贯变点检验的发展现状AI 解读

Abstract Quality control charts aim at raising an alarm as soon as sequentially obtained observations of an underlying random process no longer seem to be within stochastic fluctuations prescribed by an in-control scenario. Such random processes can often be modelled using the concept of stationarity, or even independence as in most classical works. An important out-of-control scenario is the changepoint alternative, for which the distribution of the process changes at an…

采用自适应截断阈值的共形生存分析AI 解读

Summary This paper introduces an assumption-lean method that constructs valid and efficient lower predictive bounds for survival times with censored data. We build on recent work by Candès et al. (2023), whose approach first subsets the data to discard any data points with early censoring times and then uses a reweighting technique, namely, weighted conformal inference (Tibshirani et al., 2019), to correct for the distribution shift introduced by this subsetting procedure.…