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A Unified Approach to Cramer-Rao Inequalities

Andrea Cianchi Universita degli Studi di Firenze Erwin Lutwak New York University Deane Yang New York University Gaoyong Zhang New York University

Information Theory mathscidoc:1702.19002

IEEE Transactions on Information Theory, 60, (1), 643–650, 2014
A unified approach is presented for establishing a broad class of Cram\'er-Rao inequalities for the location parameter, including, as special cases, the original inequality of Cram\'er and Rao, as well as an $L^p$ version recently established by the authors. The new approach allows for generalized moments and Fisher information measures to be defined by convex functions that are not necessarily homogeneous. In particular, it is shown that associated with any log-concave random variable whose density satisfies certain boundary conditions is a Cram\'er-Rao inequality for which the given log-concave random variable is the extremal. Applications to specific instances are also provided.
Information theory, Shannon theory, entropy, Fisher information
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@inproceedings{andrea2014a,
  title={A Unified Approach to Cramer-Rao Inequalities},
  author={Andrea Cianchi, Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228035545211454539},
  booktitle={IEEE Transactions on Information Theory},
  volume={60},
  number={1},
  pages={643–650},
  year={2014},
}
Andrea Cianchi, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. A Unified Approach to Cramer-Rao Inequalities. 2014. Vol. 60. In IEEE Transactions on Information Theory. pp.643–650. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228035545211454539.
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