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纵向网络数据的半参数建模与分析AI 解读

We introduce a semiparametric latent space model for analyzing longitudinal network data. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter by adjusting for the baseline nuisance component. Estimation is accomplished through a one-step update estimator and an appropriately penalized maximum likelihood estimator. We derive oracle error…

Abstract We study a fixed-T panel data logit model for ordered outcomes that accommodates fixed effects and state dependence. We provide identification results for the autoregressive parameter, regression coefficients, and the threshold parameters in this model. Our results require only four observations on the outcome variable. We provide conditions under which a composite conditional maximum likelihood estimator is consistent and asymptotically normal. We use our estimator…

图模型伪似然估计量的存在性与唯一性AI 解读

Summary Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high-dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for existence of the estimators, especially in comparison with the classical full covariance model. For undirected Gaussian graphical models, the minimum sample size required for the existence of maximum likelihood estimators had been an open question for…

交叉随机效应 probit 模型的一致且可扩展复合似然估计AI 解读

Summary Estimation of crossed random effects models commonly incurs computational costs that grow faster than linearly in the sample size $ N $, often as fast as $ \Omega(N^{3/2}) $, making them unsuitable for large datasets. For non-Gaussian responses, integrating out the random effects to obtain a marginal likelihood poses significant challenges, especially for high-dimensional integrals for which the Laplace approximation may not be accurate. In this article we develop a…

期望的光滑函数之无偏蒙特卡洛估计：迈向自动化方法AI 解读

Abstract Given a smooth function $ f $, we develop a general approach to turn Monte Carlo samples with expectation $ m $ into an unbiased estimate of $ f(m) $. Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of $ f $ and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters (which depend on $ m $) automatically, with a view to making the whole…

兼顾多样性与异质受欢迎程度的超图建模AI 解读

While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, that is, those between two individuals.This article addresses the less studied, though commonly encountered, polyadic relations that can involve more than two individuals.In particular, we propose a new latent space model for hypergraphs using determinantal point processes,…

采用惩罚最大似然的反卷积密度估计AI 解读

Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all infinite-dimensional deconvolution methods in the literature use Fourier transformations. These methods are mathematically neat, but unstable, and produce bad estimates when signal-noise ratio or sample size are low. A popular alternative is to maximize penalized likelihood for a finite-dimensional basis expansion of the…

复合似然与随机逼近的结合AI 解读

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inferences when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of…

矩阵 GARCH 模型：推断与应用AI 解读

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use…

网络的分组稀疏 β 模型AI 解读

Sparsity, homogeneity, and heterogeneity are three important characteristics of many real-life networks. The recently proposed Sparse β-Model divides nodes into core ones and peripheral ones to accommodate sparsity, but the parameters of core nodes are assumed to be of similar magnitude, which may not be in line with applications. In this article, we propose the Group Sparse β-Model that splits the core nodes into groups and assumes different orders of magnitude of…

Summary This paper develops a closed-form non-parametric estimator of the conditional distribution function for a binary outcome variable given an unobserved latent variable. This type of function is commonly used in models that involve measurement error and dynamic models with agent-specific unobserved heterogeneity. This paper presents a consistent extremum sieve estimator with the following advantages: (i) it has a closed-form expression for all the sieve coefficients,…

交叉随机效应广义线性混合模型中最大似然估计量的渐近分布AI 解读

Generalized linear mixed models (GLMM) with crossed random effects is infamously known to present major challenges not only computationally but also theoretically. In fact, to date only consistency of the maximum likelihood estimators (MLE) has been proved for GLMM with crosses random effects. We introduce a new technique in asymptotic analysis built on a second-order Laplace approximation (LA) of a conditional expectation, whose coefficients are carefully evaluated. The LA…

低频扩散数据的统计算法：偏微分方程方法AI 解读

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of the likelihood and its gradient, and computational methods have thus far largely resorted to expensive simulation-based techniques. In this article, we propose a new computational approach which is motivated by PDE theory and is built…

依赖关系中的BELIEF：以二元数据的线性性质重思广义线性模型AI 解读

Two linearly uncorrelated binary variables must be also independent because nonlinear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they…

跨时区股票收益的大型验证性动态因子模型AI 解读

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an Expectation Maximization (EM) algorithm (QML-all-res). Our estimators are consistent and…

有限混合模型的惩罚估计AI 解读

Economists often model unobserved heterogeneity using finite mixtures. In practice, the number of mixture components is rarely known. Model parameters lack point-identification if the estimation includes too many components, thus invalidating the classic properties of maximum likelihood estimation. I propose a penalized likelihood method to estimate finite mixtures with an unknown number of components. The resulting Order-Selection-Consistent Estimator (OSCE) consistently…

使用非线性筛方法推断时间序列非参数条件矩限制AI 解读

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series…

边际均值效应与边际分位数效应估计的半参数方法AI 解读

We consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance,…

采用最优损失函数的深度回归学习AI 解读

In this article, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal…

高维矩阵因子模型的准最大似然估计AI 解读

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator…

独立冲击的核最大似然统计识别及全球原油市场应用AI 解读

Independent component analysis has emerged as a promising approach for revealing structural relationships in multivariate dynamic systems, particularly in scenarios with limited knowledge of causal patterns. This article introduces a robust kernel-based maximum likelihood (KML) estimation method that accommodates the distributional characteristics of the structural sources of data variation. Our Monte Carlo study demonstrates the superior performance of the KML estimator…

具有互惠性的有向网络建模AI 解读

Summary Asymmetric relational data are becoming increasingly prevalent in diverse fields, underscoring the need for developing directed network models to address the complex challenges posed by the unique structure of such data. Unlike undirected models, directed models can capture reciprocity, the tendency of nodes to form mutual links. This work addresses a fundamental question: what is the effective sample size for modelling reciprocity? We examine this question by…

函数型加速失效时间模型的有效估计AI 解读

Summary We propose a functional accelerated failure time model to characterize the effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the…

双层删失生存数据的半参数筛估计AI 解读

Summary Disease registry data provide important information on the progression of disease conditions. However, reports of death or drop-out of patients enrolled in the registry are always subject to a noticeable delay. Reporting delays, together with the administrative censoring that arises from a freeze date in data collection, lead to two layers of right censoring in the data. The first layer results from random drop-out and acts on the survival time. The second layer is…