Title: Parameter Estimation for Thurstone Choice Models,
Abstract: We consider the estimation accuracy of individual strength parameters of a
Thurstone choice model when each input observation consists of a choice of one
item from a set of two or more items (so called top-1 lists). This model
accommodates the well-known choice models such as the Luce choice model for
comparison sets of two or more items and the Bradley-Terry model for pair
comparisons.
We provide a tight characterization of the mean squared error of the maximum
likelihood parameter estimator. We also provide similar characterizations for
parameter estimators defined by a rank-breaking method, which amounts to
deducing one or more pair comparisons from a comparison of two or more items,
assuming independence of these pair comparisons, and maximizing a likelihood
function derived under these assumptions. We also consider a related binary
classification problem where each individual parameter takes value from a set
of two possible values and the goal is to correctly classify all items within a
prescribed classification error.