On the Bickel–Rosenblatt test of goodness-of-fit for the residuals of autoregressive processes

• Published in: Probability and statistics Vol. 23; pp. 464 - 491
• Main Authors: Lagnoux, Agnès, Nguyen, Thi Mong Ngoc, Proïa, Frédéric
• Format: Journal Article
• Language: English
• Published: EDP Sciences 2019
• Subjects: 62F03; 62F12; 62G08; 62M10; Autoregressive process; Bickel–Rosenblatt statistic; goodness-of-fit; hypothesis testing; Mathematics; nonparametric estimation; Parzen–Rosenblatt density estimator; residual process; Statistics; Statistics Theory; residual process; hypothesis testing; nonparametric estimation; Autoregressive process; Parzen–Rosenblatt density estimator; goodness-of-fit; Bickel–Rosenblatt statistic

We investigate in this paper a Bickel–Rosenblatt test of goodness-of-fit for the density of the noise in an autoregressive model. Since the seminal work of Bickel and Rosenblatt, it is well-known that the integrated squared error of the Parzen–Rosenblatt density estimator, once correctly renormalize...