Abstract
AbstractThe ranking of objects is widely used to rate their relative quality or relevance across multiple assessments. Beyond classical rank aggregation, it is of interest to estimate the usually unobservable latent signals that inform a consensus ranking. Under the only assumption of independent assessments, which can be incomplete, we introduce indirect inference via convex optimization in combination with computationally efficient Poisson Bootstrap. Two different objective functions are suggested, one linear and the other quadratic. The mathematical formulation of the signal estimation problem is based on pairwise comparisons of all objects with respect to their rank positions. Sets of constraints represent the order relations. The transitivity property of rank scales allows us to reduce substantially the number of constraints associated with the full set of object comparisons. The key idea is to globally reduce the errors induced by the rankers until optimal latent signals can be obtained. Its main advantage is low computational costs, even when handling $$n < < p$$
n
<
<
p
data problems. Exploratory tools can be developed based on the bootstrap signal estimates and standard errors. Simulation evidence, a comparison with the state-of-the-art rank centrality method, and two applications, one in higher education evaluation and the other in molecular cancer research, are presented.
Funder
Medical University of Graz
Publisher
Springer Science and Business Media LLC
Subject
Computer Networks and Communications,Computer Science Applications,Information Systems
Reference37 articles.
1. Alvo M, Yu PLH (2014) Statistical methods for ranking data. Springer, New York
2. Babu GJ, Pathak PK, Rao CR (1999) Second-order correctness of the Poisson bootstrap. Ann Stat 27(5):1666–1683
3. Bradley RA, Terry ME (1955) Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika 39, 3/4, 324–345
4. de Borda JC. (1781) Mémoire sur les Élections au Scrutiny. Histoire de l’Acaémie Royal des Sciences, Paris
5. Chamandy N, Muralidharan O, Najmi A, Naidu S (2012) Estimating Uncertainty for Massive Data Streams. Technical Report, Google