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Optimal tests for homogeneity of covariance, scale, and shape
 J. Multivariate Anal
, 2008
"... The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic cont ..."
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The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic context of multivariate Gaussian models. And the modified likelihood ratio tests (MLRT) that are used in everyday practice are known to be highly sensitive to violations of Gaussian assumptions. In this paper, we provide a complete and systematic study of the problem, and propose test statistics which, while preserving the optimality features of the MLRT under multinormal assumptions, remain valid under unspecified elliptical densities with finite fourthorder moments. As a first step, the Le Cam LAN approach is used for deriving locally and asymptotically optimal testing procedures φ (n) f for any specified mtuple of radial densities f = (f1,..., fm). Combined with an estimation of the m densities f1,..., fm, these procedures can be used to construct adaptive tests for the problem. Adaptive tests however typically require very large samples, and pseudoGaussian tests—namely, tests that are locally and asymptotically optimal at Gaussian densities while remaining valid under a much broader class of distributions—in general are preferable. We therefore construct two pseudoGaussian modifications of the Gaussian version φ (n) N of the optimal test φ (n) f. The first one, φ
Multiple antenna cyclostationary spectrum sensing based on the cyclic correlation significance test
 IEEE J. Sel. Areas Commun
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A New Scheme for Monitoring Multvariate Process Dispersion
, 2009
"... Construction of control charts for multivariate process dispersion is not as straightforward as for the process mean. Because of the complexity of out of control scenarios, a general method is not available. In this dissertation, we consider the problem of monitoring multivariate dispersion from tw ..."
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Construction of control charts for multivariate process dispersion is not as straightforward as for the process mean. Because of the complexity of out of control scenarios, a general method is not available. In this dissertation, we consider the problem of monitoring multivariate dispersion from two perspectives. First, we derive asymptotic approximations to the power of Nagao’s test for the equality of a normal dispersion matrix to a given constant matrix under local and fixed alternatives. Second, we propose various unequally weighted sum of squares estimators for the dispersion matrix, particularly with exponential weights. The new estimators give more weights to more recent observations and are not exactly Wishart distributed. Satterthwaite’s method is used to approximate the distribution of the new estimators. By combining these two techniques based on exponentially weighted sums of squares and Nagao’s test, we are able to propose a new control scheme MTNT, which is easy to implement. The control limits are easily calculated since they only depend on the dimension of the process and the desired in control average run length. Our simulations show that compared with schemes based on the likelihood ratio test and the sample generalized variance, MTNT has the shortest out of control average run length for a variety of out of control scenarios, particularly when process variances increase.