Semiparametric estimation of the random utility model with rank-ordered choice data

We propose semiparametric methods for estimating random utility models using rank-ordered choice data. Our primary method is the generalized maximum score (GMS) estimator. With partially rank-ordered data, the GMS estimator allows for arbitrary forms of interpersonal heteroskedasticity. With fully rank-ordered data, the GMS estimator becomes considerably more flexible, allowing for random coefficients and alternative-specific heteroskedasticity and correlations. The GMS estimator has a non-standard asymptotic distribution and a convergence rate of N−1∕3. We proceed to construct its smoothed version which is asymptotically normal with a faster convergence rate of N−d∕(2d+1), where d≥2 increases in the strength of smoothness assumptions.