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arXiv · 1705.00136

Parameter Estimation for Thurstone Choice Models

Milan Vojnovic·Se-Young Yun
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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.

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Milan Vojnovic, Se-Young Yun. 2017-04-29. Parameter Estimation for Thurstone Choice Models. https://arxiv.org/abs/1705.00136

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