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凸性约束单指标模型中的半参数效率AI 解读

We consider estimation and inference in a single-index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least-square estimator (CLSE) for both the parametric and the nonparametric components given independent and identically distributed observations. We prove the consistency and find the rates of convergence of the CLSE when the errors are assumed to have only q≥2 moments and are allowed to depend on the covariates. When…

异方差与重尾误差下的最小二乘估计AI 解读

We consider least squares estimation in a general nonparametric regression model where the error is allowed to depend on the covariates. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the error has a uniformly bounded conditional variance and has only finitely many moments. Our upper bound on the rate of…