In this correspondence, we propose an efficient estimator of optimal memory (averaging interval) for discrete-time finite impulse response (FIR) filters in state-space. Its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics. Testing by the two-state polynomial model has shown a very good correspondence with predicted values. Even in the worst case of the harmonic model, the estimator demonstrates practical applicability.

a b s t r a c tIn this paper, the problem of estimating the precision matrix of a multivariate Kotz type model is considered. First, using the quadratic loss function, we prove that the unbiased estimator α 0 A −1 , where A denotes the sample sum of product matrix, is dominated by a better constant multiple of A −1 , denoted by α 0 A −1 . Secondly, a new class of shrinkage estimators of −1 is proposed. Moreover, the risk functions of α 0 A −1 , α 0 A −1 and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates α 0 A −1 , under the quadratic loss function. A simulation study is carried out which confirms these results. Improved estimator of tr( −1 ) is also obtained.Published by Elsevier Inc.

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Abstract. In this paper, we introduce a new subclass of matrix variate elliptically contoured distributions that are obtained as a scale mixture of matrix variate Cauchy distribution and exponential distribution. We investigate its properties, such as stochastic representation and characteristic function. Unlike Cauchy distribution, it is shown that the generating variate of the new distribution possesses finite moments. The distributions of the unbiased estimators of μ and Σ are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.

In this paper, the problem of estimating the precision matrix of a multivariate Pearson type II-model is considered. A new class of estimators is proposed. Moreover, the risk functions of the usual and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates the MLE and the unbiased estimator, under the quadratic loss function. A simulation study is carried out and confirms these results. Improved estimator of tr(Σ −1 ) is also obtained.