期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 104, 期 1, 页码 101-114出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2011.07.002
关键词
Stationary process; Goodness-of-fit tests; Kernel estimate; Smoothed periodogram; Weak convergence under the alternative
资金
- Collaborative Research Center Statistical modeling of nonlinear dynamic processes of the German Research Foundation (DFG) [SFB 823]
In a recent paper, Eichler (2008) [11] considered a class of non- and semiparametric hypotheses in multivariate stationary processes, which are characterized by a functional of the spectral density matrix. The corresponding statistics are obtained using kernel estimates for the spectral distribution and are asymptotically normally distributed under the null hypothesis and local alternatives. In this paper, we derive the asymptotic properties of these test statistics under fixed alternatives. In particular, we also show weak convergence but with a different rate compared to the null hypothesis. We also discuss potential statistical applications of the asymptotic theory by means of a small simulation study. (C) 2011 Elsevier Inc. All rights reserved.
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