Working Papers

Asymptotic Theory Under Network Stationarity

This paper develops an asymptotic theory for network data based on the concept of network stationarity that explicitly relates the network topology to the dependence among network entities. The framework utilizes a classifier function to assign classes to vertex pairs, and network stationarity assumes that conditional covariances depend only on the assigned class. An asymptotic theory is developed for a growing network, including laws of large numbers, an autocovariance function consistency result, and a central limit theorem, where a large portion of assumptions is random graph regularity conditions, particularly those on class sizes. The weak dependence assumptions use conditional strong mixing adapted to networks. The proposed framework is illustrated through an application to microfinance data of 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.

Work in Progress

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

Network Dependence Counterfactuals and Their Estimation Using Machine Learning

This paper introduces a new concept of network dependence counterfactuals. While counterfactual measures of outcome variables are well-understood, counterfactual dependence between outcome variables has not been considered. In this paper we exploit the network stationarity assumption allowing to estimate, given a single network observation, the counterfactual covariance between outcome variables of any two network entities under a given hypothetical network structure. We further propose a more flexible estimation procedure using machine learning algorithms. As an application, we suggest a series of vertex and edge influence and network robustness measures and illustrate them on microfinance data from Indian villages.