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.

Conditional Distribution Model Specification Testing Using Chi-Square Goodness-of-Fit Tests (with Miguel A. Delgado)

This article proposes a Pearson goodness-of-fit test for the specification of parametric conditional distribution functions. The test leverages the fact that the sample frequencies of the Rosenblatt-transformed dependent variable observations, grouped into a partition of the unit interval, is distributed as a multinomial random vector with known parameters, independently of the explanatory variable observations. It can be interpreted as a Pearson statistic for testing independence in a contingency table formed by the cross-classification of the Rosenblatt-transformed dependent variable with the explanatory variables observations. The proposed tests are invariant to data-dependent groupings, similar to the classical Pearson test for marginal distribution specifications. A Monte Carlo study demonstrates that the new tests exhibit excellent size accuracy, comparable to existing tests implemented with bootstrap techniques, while being more robust in terms of power when the dimensionality of the explanatory variable vector is high.

Latent Position-Based Modeling of Parameter Heterogeneity

This paper proposes to model parameter heterogeneity using the Generalized Random Dot Product Graph model and the underlying latent positions. Individual-specific parameter heterogeneity is modeled using the Stochastic Block Model and its extensions. For pair-specific parameter heterogeneity, a new procedure is developed that requires the number of distinct latent distances between unobserved communities to be low. It is proven that the heterogeneity pattern can be completely recovered asymptotically. A statistical test is provided for the assumption on the number of distinct latent distances. The proposed methods are illustrated using data on a microfinance program and S&P 500 component stocks.

Work in Progress

Network Dependence Counterfactuals

Machine Learning-Based T-test for the Goodness-of-Fit of Conditional Moment Restriction Models (with Antonio Raiola, Joël Terschuur, and Luke Taylor)

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