Semiparametric Mixed Transformation Models for Ranking Data with An Application

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We provide an estimation procedure for the parameters in a mixed-e®ects
transformation model when responses are only observed in the form of rankings within a
cluster. Such data are widely seen in epidemiological studies, population pharmacokinetics
and economics. The model allows the transformations to be di®erent across di®erent clus-ter and the estimation procedure avoids estimating those in¯nitely dimensional nuisance
parameters. A three-stage Markov chain Monte Carlo stochastic approximation (MCMC-SA) algorithm is developed to ¯nd the solutions to the estimating equation. Monte Carlo
simulation results show that our estimation procedure behaves well with small and mod-erate sample size. We used the model and the estimation procedure to show that the
racetrack betting market in Hong Kong is not semi-strong e±cient

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关键词：Application Parametric formation transform semipara procedure provide across within chain