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7. Statistical Analysis of Circular Data

7. Statistical Analysis of Circular Data REVIEWS [Part 1, integral can be replaced by the NTM. As might be expected, the authors' favourite method is always the best of the restricted field considered. The authors seem unaware of many of the connections with work in the simulation community and fail even to consider the criticisms in that community of the main measure of uniformity they use, the discrepancy, which lacks invariance to rotations of the co-ordinate space. In short, this is a book by believers (in the NTM) for believers. The typesetting of this volume (especially its tables) is so poorly designed that I found it trying to read. References Niederreiter, H. (1992) Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: Society for Industrial and Applied Mathematics. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1992) Numerical Recipes in C, 2nd edn. Cambridge: Cambridge University Press. B. D. Ripley Oxford University 7. Statistical Analysis of Circular Data. By N. I. Fisher. ISBN 0 521 35018 2. Cambridge University Press, Cambridge, 1993. £35.00. This book may be regarded as a companion volume to Statistical Analysis of Spherical Data (Fisher et aI., 1987),although the approach adopted is somewhat different, with greater emphasis on data display and the use of modern methodology such as the bootstrap, permutation distri­ butions and nonparametric smoothing to cope with otherwise intractable distributional problems. The introduction contains a fascinating illustrated account of some of the early history of circular statistics. The chapter on descriptive methods introduces the usual techniques, from angular histograms and rose diagrams to angular stem-and-leaf diagrams and trigonometric moments, and also includes basic density estimation methods in the context of the circle. A wide range of data sets, listed in an appendix, are used as examples, both for exploratory analyses such as uniformity plots and symmetry plots, and also for significance tests. Modern non parametric methods are used extensively; my preference would have been for the general final Chapter 8 on permutation distributions and bootstrapping to occur rather earlier, as I have a preference for referring back to previous material, rather than the constant references forwards to Chapter 8. This is, however, only a minor quibble. There is a summary of methodology of relatively recent provenance, much of it due to the author, for dealing with linear-circular and circular-circular correlation, and for the estimation and testing problems arising from the associated regression models. The account of time series methods for circular variables includes linear and circular autoregressive moving average models which were introduced only recently. Chapter 7 here is a clear and concise exposition with a good selection of relevant diagrams. The author even finds room for a discussion of the spatial analysis of directional data. The contents of this book are accessible to the non-statistician with an interest in directional applications, and the range of topics covered is sufficiently wide that it is also a valuable addition to the statistician's bookshelf. It is a useful summary of both standard material and some fairly recent developments, using examples from the earth sciences as well as biology. 12 years on, it covers much more ground than Batschelet (1981). References Batschelet, E. (1981) Circular Statistics in Biology. London: Academic Press. Fisher, N. 1., Lewis, T. and Embleton, B. J. J. (1987) Statistical Analysis oj Spherical Data. Cambridge: Cambridge University Press. M. J. Prentice University of Edinburgh http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Royal Statistical Society Series A (Statistics in Society) Oxford University Press

7. Statistical Analysis of Circular Data

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References (2)

Copyright
© 1995 Royal Statistical Society
ISSN
0964-1998
eISSN
1467-985X
DOI
10.2307/2983422
Publisher site
See Article on Publisher Site

Abstract

REVIEWS [Part 1, integral can be replaced by the NTM. As might be expected, the authors' favourite method is always the best of the restricted field considered. The authors seem unaware of many of the connections with work in the simulation community and fail even to consider the criticisms in that community of the main measure of uniformity they use, the discrepancy, which lacks invariance to rotations of the co-ordinate space. In short, this is a book by believers (in the NTM) for believers. The typesetting of this volume (especially its tables) is so poorly designed that I found it trying to read. References Niederreiter, H. (1992) Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: Society for Industrial and Applied Mathematics. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1992) Numerical Recipes in C, 2nd edn. Cambridge: Cambridge University Press. B. D. Ripley Oxford University 7. Statistical Analysis of Circular Data. By N. I. Fisher. ISBN 0 521 35018 2. Cambridge University Press, Cambridge, 1993. £35.00. This book may be regarded as a companion volume to Statistical Analysis of Spherical Data (Fisher et aI., 1987),although the approach adopted is somewhat different, with greater emphasis on data display and the use of modern methodology such as the bootstrap, permutation distri­ butions and nonparametric smoothing to cope with otherwise intractable distributional problems. The introduction contains a fascinating illustrated account of some of the early history of circular statistics. The chapter on descriptive methods introduces the usual techniques, from angular histograms and rose diagrams to angular stem-and-leaf diagrams and trigonometric moments, and also includes basic density estimation methods in the context of the circle. A wide range of data sets, listed in an appendix, are used as examples, both for exploratory analyses such as uniformity plots and symmetry plots, and also for significance tests. Modern non parametric methods are used extensively; my preference would have been for the general final Chapter 8 on permutation distributions and bootstrapping to occur rather earlier, as I have a preference for referring back to previous material, rather than the constant references forwards to Chapter 8. This is, however, only a minor quibble. There is a summary of methodology of relatively recent provenance, much of it due to the author, for dealing with linear-circular and circular-circular correlation, and for the estimation and testing problems arising from the associated regression models. The account of time series methods for circular variables includes linear and circular autoregressive moving average models which were introduced only recently. Chapter 7 here is a clear and concise exposition with a good selection of relevant diagrams. The author even finds room for a discussion of the spatial analysis of directional data. The contents of this book are accessible to the non-statistician with an interest in directional applications, and the range of topics covered is sufficiently wide that it is also a valuable addition to the statistician's bookshelf. It is a useful summary of both standard material and some fairly recent developments, using examples from the earth sciences as well as biology. 12 years on, it covers much more ground than Batschelet (1981). References Batschelet, E. (1981) Circular Statistics in Biology. London: Academic Press. Fisher, N. 1., Lewis, T. and Embleton, B. J. J. (1987) Statistical Analysis oj Spherical Data. Cambridge: Cambridge University Press. M. J. Prentice University of Edinburgh

Journal

Journal of the Royal Statistical Society Series A (Statistics in Society)Oxford University Press

Published: Dec 5, 2018

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