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Cressie–Read Power‐Divergence Statistics for Non‐Gaussian Vector Stationary Processes
Author(s) -
OGATA HIROAKI,
TANIGUCHI MASANOBU
Publication year - 2009
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00618.x
Subject(s) - mathematics , statistic , divergence (linguistics) , autocorrelation , empirical likelihood , statistics , likelihood ratio test , test statistic , asymptotic distribution , gaussian , scan statistic , asymptotic analysis , statistical hypothesis testing , confidence interval , philosophy , linguistics , physics , quantum mechanics , estimator
. For a class of vector‐valued non‐Gaussian stationary processes, we develop the Cressie–Read power‐divergence (CR) statistic approach which has been proposed for the i.i.d. case. The CR statistic includes empirical likelihood as a special case. Therefore, by adopting this CR statistic approach, the theory of estimation and testing based on empirical likelihood is greatly extended. We use an extended Whittle likelihood as score function and derive the asymptotic distribution of the CR statistic. We apply this result to estimation of autocorrelation and the AR coefficient, and get narrower confidence intervals than those obtained by existing methods. We also consider the power properties of the test based on asymptotic theory. Under a sequence of contiguous local alternatives, we derive the asymptotic distribution of the CR statistic. The problem of testing autocorrelation is discussed and we introduce some interesting properties of the local power.