Semiparametric Analysis of Discrete Response: Asymptotic Properties of Maximum Score

This paper is concerned with the estimation of the model MED ( y 1 x) = x/3 from a random sample of observations on (sgn y, x). Manski (1975) introduced the maximum score estimator of the normalized parameter vector /3 * = /3/]]8]]. In the present paper, strong consistency is proved. It is also proved that the maximum score estimate lies outside any fixed neighborhood of p * with probability that goes to zero at exponential rate. 1