This thesis contributes to the development of the Network Scale-up Method (NSUM). This technique emerged as an alternative to traditional survey methods and estimates the size of a group from a population using Aggregated Relational Data, which consists of the number of contacts that belong to several groups.  NSUM leverages the number of connections of the participants’ surrounding neighborhood, effectively increasing the fraction of the network for which data are available. In addition, the use of ARD preserves the privacy of the participants and therefore increases participation and honesty, mitigating biases of traditional surveys. Due to the advantages of NSUM, it has motivated a wide range of applications in public health, epidemiology, and estimation of sensitive groups. and quantifying the impact of disasters.

Although NSUM techniques have been applied to a wide range of problems of public relevance since their introduction nearly four decades ago, several important research challenges remain unresolved. This thesis is a compendium of publications that address these previous research questions through four complementary directions. The first direction is the empirical evaluation of existing NSUM techniques. The second research line is the development of the theoretical foundations of NSUM and ARD methods. The third direction is the proposal of new methods. Finally, this thesis extends the application of these techniques to a new domain.

The first part provides an exhaustive evaluation of the performance of most of the NSUM estimators through an extensive simulation environment. The empirical comparison reveals the impact of the biases, the design of the survey, and the sample size on the existing NSUM estimators. The second part develops a theoretical framework for analyzing the error of the NSUM estimators, providing error bounds under adversarial scenarios and random structures. The third part proposes a framework for estimating temporal trends from ARD and provides a theoretical comparison of its advantages over traditional survey methods.  The fourth part proposes robust versions of existing NSUM estimators by replacing the sample means with alternative location estimators. These versions mitigate the sensitivity to anomalous responses due to the use of sample means in the traditional NSUM techniques. The fifth part extends the application of NSUM to estimating voting intention in electoral processes, outperforming several well-established polling institutions using smaller sample sizes. The final part implements NSUM to measure attributes of virtual networks used for content distribution, decentralized payment systems, and blockchain technologies. This framework estimates network attributes using only the information of a small number of nodes, considerably reducing the intrusiveness and computational cost of existing measurement techniques that require exhaustive identification of the entire network.

About Sergio Díaz Aranda

Sergio Díaz-Aranda is a final-year PhD student in Mathematical Engineering at the IMDEA Networks Institute and Universidad Carlos III de Madrid, working under the supervision of Prof. Antonio Fernández Anta. He received his MSc and BSc in Mathematics at Universidad Complutense de Madrid, Spain. His research focuses on statistical inference from partial network data in low-resource settings.

PhD Thesis Advisor:  Dr. Antonio Fernández Anta, Deputy Director at IMDEA Software Institute & Part-time Research Professor at IMDEA Networks Institute / Rosa Elvira Lillo, Universidad Carlos III de Madrid

University: Universidad Carlos III de Madrid (UC3M), Spain

Doctoral Program: Mathematical Engineering

PhD Committee members:

•  President: Miranda Lubbers, Professor, Universitat Autònoma de Barcelona
•  Secretary: María del Mar Rueda, Professor, Universidad de Granada
•  Panel member: Carlos Baquero, Professor, Universidade do Porto