By Barry C. Arnold, Ashis SenGupta (auth.), Martin T. Wells, Ashis SenGupta (eds.)

The current quantity involves papers written via scholars, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from a number of international locations, and covers various examine themes which he enjoys and contributed immensely to.

**Read Online or Download Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka PDF**

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**Extra info for Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka**

**Sample text**

Though the earth is unequivocally warming, the geographical patchiness of the recent climate change is evident since it has been reported that the Antarctic Peninsula (the northern most part of the mainland of Antarctica) is one of the rapid warming areas in recent 50 years (see [4]). Since the temperature records at industrial areas may be masked by both the increased concentrations of shortlived sulphate aerosols and the heating of urban meteorological stations, it has been suggested by [13] that the temperature trends of Antarctic stations are a particularly important indicator of climate change.

Z 0t k Z t k 0 / is finite for k; k 0 D 1; : : : ; p. i; j /th element given by lim is positive definite. Furthermore, we assume ˙" D sum of squares is given by: SD 1 T X 2 2 IN for simplicity. 1. Suppose « D fBm;n ; k0 ; k1 ; Âl0 ; Âl1 g, with m D 1; : : : ; N I n D 1; : : : ; rI k D 1; : : : ; pI l D 1; : : : ; q. The least square estimates «O are asymptotically normally distributed with mean « and with covariance matrix given by: 34 X. S. Z t k/ 0 W "t l /: t DhC1 Proof. 1, we follow the method of [8] given for univariate regression models with ARMA errors.

It is shown that, under constraints on some moments along some fixed directions, and using Kullback–Leibler information as measure, the closest distribution to any predetermined one on S p 1 , has the GvMF form. Lower bounds for the Kullback–Leibler information in this context are also provided. Several connections between GvMF and other directional or linear distributions are given. GvMF distributions can be re-expressed in terms of generalized von Mises distributions when p D 2. GvMF distributions arise as offset multivariate normal distributions, as offset singular normal distributions and as offset distributions from an exponential spherical type of distributions.