This paper proposes a new semiparametric estimator of models where the response random variable is a fraction. The estimator is constructed by optimizing a semiparametric quasi-maximum likelihood that utilizes kernel smoothing. Under suitable conditions, the consistency and asymptotic normality of the proposed estimator is established allowing for data-driven bandwidth choices as well as random trimming, and its flexibility and robustness are showcased in a Monte Carlo experiment and an empirical application.