Random Sieve Likelihood and General Regression Models
针对半参数回归模型Y=f(θ,X,ε)，提出一种基于随机水平集构建剖面似然的新估计方法，适用于高维数据、非参数随机效应和右删失数据等场景，模拟和渐近分析验证了其有效性。
Abstract Consider a semiparametric regression model Y = f(θ, X, ϵ), where f is a known function, θ is an unknown vector, ϵ consists of a random error and possibly of some unobserved variables, and the distribution F(·) of (ϵ, X) is unspecified. This article introduces, in a general setting, new methodology for estimating θ and F(·). The proposed method constructs a profile likelihood defined on random-level sets (a random sieve). The proposed method is related to empirical likelihood but is more generally applicable. Four examples are discussed, including a quadratic model, high-dimensional semiparametric regression, a nonparametric random-effects model, and linear regression with right-censored data. Simulation results and asymptotic analysis support the utility and effectiveness of the proposed method.