Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

作者：Banks H T^*; Catenacci Jared; Hu Shuhua

来源：SIAM-ASA Journal on Uncertainty Quantification, 2015, 3(1): 417-433.

DOI：10.1137/140972639

• least-squares method
• Prohorov metric
• model selection criterion
• consistency
• pointwise asymptotic normality
• confidence band

We consider probability measure estimation in a nonparametric model using a least-squares approach under the Prohorov metric framework. We summarize the computational methods and related convergence results that were recently developed by our group. New results are presented on the bias and the variance due to the approximation and new pointwise asymptotic normality of the approximated probability measure estimator. We propose the use of a model selection criterion to balance the bias and the variance, and compare the new pointwise confidence bands constructed using the asymptotic normality results with those obtained by Monte Carlo simulations.

• 出版日期2015