Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator

This paper is concerned with the estimation of the model MED(y|x) = xβ from a random sample of observations on (sgn y, x). Manski (1975) introduced the maximum score estimator of the normalized parameter vector $\text{β}{}^1\text{= β/?β?}$. In the present paper, strong consistency is proved. It is also proved that the maximum score estimate lies outside any fixed neighborhood of β¹ with probability that goes to zero at exponential rate.