Asymptotic normality of quadratic estimators

作者：Robins James M^*; Li Lingling; Tchetgen Eric Tchetgen; van der Vaart Aad

来源：Stochastic Processes and Their Applications, 2016, 126(12): 3733-3759.

DOI：10.1016/j.spa.2016.04.005

• Quadratic functional
• Projection estimator
• Rate of convergence
• U-statistic

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

• 出版日期2016-12