Econometric Models of Network Formation

This article provides a selective review of the recent literature on econometric models of network formation. I start with a brief exposition on basic concepts and tools for the statistical description of networks; then I offer a review of dyadic models, focusing on statistical models on pairs of nodes, and I describe several developments of interest to the econometrics literature. I also present a discussion of nondyadic models in which link formation might be influenced by the presence or absence of additional links, which themselves are subject to similar influences. This argument is related to the statistical literature on conditionally specified models and the econometrics of game theoretical models. I close with a (nonexhaustive) discussion of potential areas for further development.

Nonstandard conditionally specified models for nonignorable missing data

Data analyses typically rely upon assumptions about the missingness mechanisms that lead to observed versus missing data, assumptions that are typically unassessable. We explore an approach where the joint distribution of observed data and missing data are specified in a nonstandard way. In this formulation, which traces back to a representation of the joint distribution of the data and missingness mechanism, apparently first proposed by J. W. Tukey, the modeling assumptions about the distributions are either assessable or are designed to allow relatively easy incorporation of substantive knowledge about the problem at hand, thereby offering a possibly realistic portrayal of the data, both observed and missing. We develop Tukey’s representation for exponential-family models, propose a computationally tractable approach to inference in this class of models, and offer some general theoretical comments. We then illustrate the utility of this approach with an example in systems biology.

Bivariate Dynamic Weighted Survival Entropy of Order 𝛼

Recently, G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini [G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini, On dynamic weighted survival entropy of order α, Comm. Statist. Theory Methods 46 2017, 5, 2139–2150] proposed a measure of uncertainty based on the survival function called weighted survival entropy of order α. They have also introduced the dynamic form of a measure called dynamic weighted survival entropy of order α and studied various properties in the context of reliability modeling. In this paper, we extend these measures into the bivariate setup and study its properties. We also look into the problem of extending the same measure for conditionally specified models. Empirical and non-parametric estimators are suggested for the proposed measure using the conditionally specified model, and the effect of the proposed estimators is illustrated using simulated and real data sets.