This paper introduces a semiparametric least squares (SLS) estimator for single-index models, which is consistent and asymptotically normal. The estimator is defined by minimizing a sample analog of the expected squared error, where the objective function involves a kernel regression estimator of the conditional expectation. The SLS estimator is shown to be consistent up to a multiplicative constant and asymptotically normal under regularity conditions. A weighted SLS (WSLS) estimator is also introduced, which achieves the semiparametric efficiency bound established by Newey (1990). The paper discusses the properties of single-index models, which include censored Tobit models, binary choice models, and duration models with unobserved heterogeneity. The SLS estimator is shown to be consistent and asymptotically normal under certain assumptions, and the WSLS estimator is shown to achieve the semiparametric efficiency bound. The paper also provides a consistent estimator for the covariance matrix and discusses the small-sample properties of the SLS estimator through a Monte Carlo experiment. The paper concludes with a discussion of future research directions.This paper introduces a semiparametric least squares (SLS) estimator for single-index models, which is consistent and asymptotically normal. The estimator is defined by minimizing a sample analog of the expected squared error, where the objective function involves a kernel regression estimator of the conditional expectation. The SLS estimator is shown to be consistent up to a multiplicative constant and asymptotically normal under regularity conditions. A weighted SLS (WSLS) estimator is also introduced, which achieves the semiparametric efficiency bound established by Newey (1990). The paper discusses the properties of single-index models, which include censored Tobit models, binary choice models, and duration models with unobserved heterogeneity. The SLS estimator is shown to be consistent and asymptotically normal under certain assumptions, and the WSLS estimator is shown to achieve the semiparametric efficiency bound. The paper also provides a consistent estimator for the covariance matrix and discusses the small-sample properties of the SLS estimator through a Monte Carlo experiment. The paper concludes with a discussion of future research directions.