Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This article investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approx- imation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.

We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation.

Graph convolutional networks (GCN) are viewed asone of the most popular representations among thevariants of graph neural networks over graph dataand have shown powerful performance in empiricalexperiments. That l2-based graph smoothing enforces the global smoothness of GCN, while (soft)l1-based sparse graph learning tends to promotesignal sparsity to trade for discontinuity. This paper aims to quantify the trade-off of GCN betweensmoothness and sparsity, with the help of a generall, ℓp-regularized (1 < p≤ 2) stochastic learning pro.posed within. While stability-based generalizationanalyses have been given in prior work for a secondderivative objectiveness function, our ℓp-regularized learning scheme does not satisfy such a smooth con.dition. To tackle this issue, we propose a novel SGD proximal algorithm for GCNs with an inexactoperator. For a single-layer GCN, we establish anexplicit theoretical understanding of GCN with the ℓp-regularized stochastic learning by analyzing thestability of our SGD proximal algorithm. We conduct multiple empirical experiments to validate ourtheoretical findings.

We propose a new unit-root test for a stationary null hypothesis H0 against a unit-root alternative H1. Our approach is nonparametric as H0 assumes only that the process concerned is I (0), without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for an I(0) process, but diverges to infinity for a process with unit roots.

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 of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and nonstandard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks. Supplementary materials for this article are available online.

Directed acyclic graph (DAG) models are widely used to represent casual relationships among random variables in many application domains. This article studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean. Such a class of non-Gaussian DAG models are fairly flexible and admit many popular distributions as special cases, including Poisson, Binomial, Geometric, Exponential, and Gamma. To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm. It first reconstructs the topological layers in a hierarchical fashion and then recovers the directed edges between nodes in different layers, which requires much less computational cost than most existing algorithms in literature. Its advantage is also demonstrated in a number of simulated examples, as well as its applications to two real-life datasets, including an NBA player statistics data and a cosmetic sales data collected by Alibaba. Supplementary materials for this article are available online.

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by iid measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this article, we consider functional linear regression with serially dependent observations of the functional predictor, when the contamination of the predictor by the white noise is genuinely functional with fully nonparametric covariance structure. Inspired by the fact that the autocovariance function of observed functional predictors automatically filters out the impact from the unobservable noise term, we propose a novel autocovariance-based generalized method-of-moments estimate of the slope function. We also develop a nonparametric smoothing approach to handle the scenario of partially observed functional predictors. The asymptotic properties of the resulting estimators under different scenarios are established. Finally, we demonstrate that our proposed method significantly outperforms possible competing methods through an extensive set of simulations and an analysis of a public financial dataset.

We develop a two-stage approach to estimate the treatment effects of dummy endogenous variables using high-dimensional instrumental variables (IVs). In the first stage, instead of using a conventional linear reduced-form regression to approximate the optimal instrument, we propose a penalized logistic reduced-form model to accommodate both the binary nature of the endogenous treatment variable and the high dimensionality of the IVs. In the second stage, we replace the original treatment variable with its estimated propensity score and run a least-squares regression to obtain a penalized logistic regression instrumental variables estimator (LIVE). We show theoretically that the proposed LIVE is root-n consistent with the true treatment effect and asymptotically normal. Monte Carlo simulations demonstrate that LIVE is more efficient than existing IV estimators for endogenous treatment effects. In applications, we use LIVE to investigate whether the Olympic Games facilitate the host nation’s economic growth and whether home visits from teachers enhance students’ academic performance. In addition, the R functions for the proposed algorithms have been developed in an R package naivereg. The Canadian Journal of Statistics 50: 795–819;

Recent studies show that advanced priors play a major role in deep generativemodels. Exemplar VAE, as a variant of VAE with an exemplar-based prior, hasachieved impressive results. However, due to the nature of model design, anexemplar-based model usually requires vast amounts of data to participate in training, which leads to huge computational complexity. To address this issue, wepropose Bayesian Pseudocoresets Exemplar VAE (ByPE-VAE), a new variant of VAE with a prior based on Bayesian pseudocoreset. The proposed prior is condi.tioned on a small-scale pseudocoreset rather than the whole dataset for reducingthe computational cost and avoiding overfitting. Simultaneously, we obtain theoptimal pseudocoreset via a stochastic optimization algorithm during VAE trainingaiming to minimize the Kullback-Leibler divergence between the prior based onthe pseudocoreset and that based on the whole dataset. Experimental results showthat ByPE-VAE can achieve competitive improvements over the state-of-the-artVAEs in the tasks of density estimation, representation learning, and generativedata augmentation. Particularly, on a basic VAE architecture, ByPE-VAE is up to 3times faster than Exemplar VAE while almost holding the performance. Code isavailable at https://github.com/Aiqz/ByPE-VAE.

High-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. Second, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. Numerical studies demonstrate promising performance and potential practical benefits of the new methods.