Hypothesis testing for a functional parameter via sample splitting

Oregon Convention Center 

For testing hypothesis on a multi-dimensional parameter associated with a time series, the self-normalization (SN) method avoids the bandwidth choice and is asymptotically distribution-free under the null. So far the literature has not provided a way of using SN for the inference of an infinite dimensional parameter. In this talk, I will propose a SN-based inference method for a functional parameter via the idea of sample splitting. The proposed statistic avoid the bandwidth choice, and are asymptotically distribution-free. Our method has wide applicability and can be used for many time series testing problems when an infinite dimensional parameter is of main interest. Through simulations, we examine their finite sample performance in comparison with some existing methods, and show that the proposed methods typically leads to more accurate size with mild loss of power.

Time Series

Infinite Dimensional Parameter

Sample Splitting

Inference 

Section on Nonparametric Statistics