Random sieve likelihood and general regression models

Consider a semiparametric regression model Y = f (theta, X, epsilon), where f is a known function, theta is an unknown vector, epsilon consists of a r andom error and possibly of some unobserved variables, and the distribution F(.) of (epsilon, X) is unspecified. This article introduces, in a general setting, new methodology for estimating theta and F(.). The proposed metho d constructs a profile likelihood defined on random-level sets (a random si eve). The proposed method is related to empirical likelihood but is more ge nerally applicable. Four examples are discussed, including a quadratic mode l, high-dimensional semiparametric regression, a nonparametric random-effec ts model, and linear regression with right-censored data. Simulation result s and asymptotic analysis support the utility and effectiveness of the prop osed method.