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On the Bickel-Rosenblatt test of goodness-of-fit for the residuals of autoregressive processes. (arXiv:1706.09811v1 [math.ST])
来源于:arXiv
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 renormalized, is
asymptotically Gaussian for independent and identically distributed (i.i.d.)
sequences. We show that the result still holds when the statistic is built from
the residuals of general stable and explosive autoregressive processes. In the
univariate unstable case, we also prove that the result holds when the unit
root is located at $-1$ whereas we give further results when the unit root is
located at $1$. In particular, we establish that except for some particular
asymmetric kernels leading to a non-Gaussian limiting distribution and a slower
convergence, the statistic has the same order of magnitude. Finally we build a
goodness-of-fit Bickel-Rosenblatt test for the true density of the no 查看全文>>