Abstract
Paired comparison data is often used to rank or order a set of items. In this paper we study a method for estimating the parameters associated with completely ordered cardinal paired comparison data. The analysis is carried out within the framework of graphical linear models but rather than using the least squares estimator, which may be difficult to analyze, we consider the average of all tree-based estimators for the connected comparison graph. The resulting estimator is a simple linear function of the sufficient statistics and has an easy to understand graph-theoretic interpretation. The statistical properties of this estimator are studied and it is shown to be unbiased, strongly consistent and asymptotically normal. Examples and numerical comparisons are provided and extensions are discussed.
| Original language | American English |
|---|---|
| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 209 |
| DOIs | |
| State | Published - Dec 2020 |
Keywords
- Incidence matrix
- Moore–Penrose inverse
- Paired comparisons
- Spanning tree
- Statistical ranking
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics