Asymptotics for L2-norm of ARCH innovation density estimator

作者：Cheng Fuxia^*; Sun Shuxia; Wen Miin Jye

来源：Journal of Statistical Planning and Inference, 2011, 141(12): 3771-3779.

DOI：10.1016/j.jspi.2011.06.013

• ARCH-time series
• Kernel density estimation
• Goodness-of-fit test
• L2-norm

In this paper we consider the asymptotic properties of the ARCH innovation density estimator. We obtain the asymptotic normality of the Bickel-Rosenblatt test statistic (based on our density estimator) under the null hypothesis, which is the same as in the case of the one sample set up (given in Bickel and Rosenblatt, 1973). We also show the strong consistency of the estimator for the true density in L2-norm.

• 出版日期2011-12