Working Papers

Asymptotic Theory Under Network Stationarity

This paper develops an asymptotic theory for network data based on the concept of network stationarity, explicitly linking network topology with the dependence between network entities. Each pair of entities is assigned a class based on a bivariate graph statistic. Network stationarity assumes that conditional covariances depend only on the assigned class. The asymptotic theory, developed for a growing network, includes laws of large numbers, consistent autocovariance function estimation, and a central limit theorem. A significant portion of the assumptions concerns random graph regularity conditions, particularly those related to class sizes. Weak dependence assumptions use conditional alpha-mixing adapted to networks. The proposed framework is illustrated through an application to microfinance data from Indian villages.

Chi-Square Goodness-of-Fit Tests for Conditional Distributions (with Miguel A. Delgado)

We propose a cross-classification rule for the dependent and explanatory variables resulting in a contingency table such that the classical trinity of chi-square statistics can be used to check for conditional distribution specification. The resulting Pearson statistic is equal to the Lagrange multiplier statistic. We also provide a Chernoff-Lehmann result for the Pearson statistic using the raw data maximum likelihood estimator, which is applied to show that the corresponding limiting distribution of the Wald statistic does not depend on the number of parameters. The asymptotic distribution of the proposed statistics does not change when the grouping is data dependent. An algorithm allowing to control the number of observations per cell is developed. Monte Carlo experiments provide evidence of the excellent size accuracy of the proposed tests and their good power performance, compared to omnibus tests, in high dimensions.

Latent Position-Based Modeling of Parameter Heterogeneity

This paper proposes to use the Generalized Random Dot Product Graph model and the underlying latent positions to model parameter heterogeneity. We discuss how the Stochastic Block Model can be directly applied to model individual parameter heterogeneity. We also develop a new procedure to model pairwise parameter heterogeneity requiring the number of distinct latent distances between unobserved communities to be low. It is proven that, asymptotically, the heterogeneity pattern can be completely recovered. Additionally, we provide three test statistics for the assumption on the number of distinct latent distances. The proposed methods are illustrated using data on a household microfinance program and the S&P 500 component stocks.

Work in Progress

Nonparametric Estimation of Low-Rank Graphons (with László Györfi and Gábor Lugosi)

Network Dependence Counterfactuals