In September 2020 I will join the University of Cambridge as an assistant professor.

**Research Fields**- Econometrics
- Machine Learning
- Network Econometrics

**References**- Miguel A. Delgado (Advisor)
- Juan Carlos Escanciano
- Gábor Lugosi
- Carlos Velasco

**Contact**- julius.vainora@uc3m.es
- +34 644 223 642

**Network Dependence and Inference**

This paper considers the problem of making valid inferences with network data. In general, data is dependent when the underlying entities form a network; however, the exact nature of the relationship between network topology and data dependence is not clear. Accounting for dependence between network entity attributes is instrumental for valid inferences, but this has received little formal treatment and tends to be neglected in practice. The main contribution of this paper is to provide a formal framework for handling the dependence of network data, giving rise to new ways of making inferences. The proposed estimators can be easily implemented in practice and require a single network observation. Laws of large numbers, consistency of autocovariance function estimators, and a central limit theorem are proven. A number of theoretical and empirical applications of the provided framework are presented.

**A Pearson Statistic for Conditional Distribution Model Checking** (with Miguel A. Delgado)

We propose an asymptotically pivotal Pearson statistic for specification testing of parametric conditional distributions. Data is grouped into a contingency table according to partitions exploiting the fact that the conditional integral transform of the dependent variable is independent of the explanatory variables. We can reproduce classical results for marginal distributions related to Pearson test using this type of partition, for example, a Chernoff-Lehmann result and the asymptotic equivalence to the likelihood ratio test and some computationally relevant alternatives. In particular, the tests are still valid when sample-dependent partitions are used, and we provide an algorithm to construct partitions with asymptotically equiprobable classes. Also, a normal approximation is valid when the number of classes in the partition is large, which is relevant when data is sparse, with some empty cells. We study the power of the test under contiguous alternatives converging to the null at the rate of \(n^{-1/2}\) or \(n^{-1/4}\), when the number of cells is fixed or diverges with the sample size respectively. The finite sample performance of the test is examined by means of a Monte Carlo experiment, where we compare Pearson test with existing omnibus alternatives.

**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.

Fall 2017–2019

**Preliminary Statistics** (Ph.D. program, Instructor)

Spring 2017–2019

**Econometrics II** (Ph.D. program, TA, Profs. Miguel A. Delgado and Carlos Velasco)

Spring 2017–2020

**Quantitative Macroeconomics** (Undergraduate program, Course support, Prof. Álvaro Escribano)

Spring 2017

**Applied Time Series Econometrics with R** (Online course review, Prof. Miguel A. Arranz)

Fall 2015–2016

**Game Theory** (Master program, TA, Prof. Francisco Marhuenda)

Spring 2016

**Econometrics** (Undergraduate program, TA, Prof. Gabriel Smagghue)