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具有依赖边的自回归网络AI 解读

Abstract We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network data. By assuming the edges of networks at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal exponential random graph models, facilitate both simulation and…

动态网络的双重异质性模型AI 解读

Analysis of networks that evolve dynamically requires the joint modelling of individual snapshots and time dynamics. This paper proposes a new flexible two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity to form ties with other nodes statically and the other to differentiate the tendency to retain existing ties over time. With n observed networks each having p…

通过随机扰动与矩估计实现 β 模型的边差分隐私估计AI 解读

A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here, we conduct an in-depth study of this trade-off for parameter estimation in the β-model (Ann. Appl. Probab. 21 (2011) 1400–1435) for edge differentially private network data released via jittering (J. R. Stat. Soc. Ser. C. Appl. Stat. 66 (2017) 481–500). Unlike most previous approaches based on maximum likelihood estimation for this network…

含噪网络中的子图密度估计AI 解读

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version…

带状时空自回归模型AI 解读

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and…

未知对角系数时空模型的广义 Yule–Walker 估计AI 解读

We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule–Walker estimation method which applies the least squares estimation to a Yule–Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations…

相依随机变量函数的极端分位数估计AI 解读

Summary We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast with the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The method proposed is semiparametric as no parametric forms are assumed on the marginal…

利用降维近似条件分布函数AI 解读

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y|X, but that of Y|θTX, where the unit vector θ is selected so that the approximation is optimal under a least-squares criterion. We show that θ may be estimated root-n consistently. Furthermore, estimation of the conditional distribution…

条件分布函数的估计方法AI 解读

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the…