Information-theoretic upper and lower bounds for statistical estimation Export

@article{citeulike:5335891, abstract = {In this paper, we establish upper and lower bounds for some statistical estimation problems through concise information-theoretic arguments. Our upper bound analysis is based on a simple yet general inequality which we call the information exponential inequality. We show that this inequality naturally leads to a general randomized estimation method, for which performance upper bounds can be obtained. The lower bounds, applicable for all statistical estimators, are obtained by original applications of some well known information-theoretic inequalities, and approximately match the obtained upper bounds for various important problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estimator to vary for different possible underlying distributions according to a predefined prior}, author = {Zhang, Tong}, booktitle = {Information Theory, IEEE Transactions on}, citeulike-article-id = {5335891}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TIT.2005.864439}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1614067}, day = {03}, doi = {10.1109/TIT.2005.864439}, journal = {Information Theory, IEEE Transactions on}, keywords = {bounds, information, risk, theory}, month = {April}, number = {4}, pages = {1307--1321}, posted-at = {2009-08-03 05:02:56}, priority = {3}, title = {Information-theoretic upper and lower bounds for statistical estimation}, url = {http://dx.doi.org/10.1109/TIT.2005.864439}, volume = {52}, year = {2006} }

TY - JOUR ID - citeulike:5335891 L3 - citeulike-article-id:5335891 N2 - In this paper, we establish upper and lower bounds for some statistical estimation problems through concise information-theoretic arguments. Our upper bound analysis is based on a simple yet general inequality which we call the information exponential inequality. We show that this inequality naturally leads to a general randomized estimation method, for which performance upper bounds can be obtained. The lower bounds, applicable for all statistical estimators, are obtained by original applications of some well known information-theoretic inequalities, and approximately match the obtained upper bounds for various important problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estimator to vary for different possible underlying distributions according to a predefined prior IS - 4 JF - Information Theory, IEEE Transactions on EP - 1321 TI - Information-theoretic upper and lower bounds for statistical estimation VL - 52 T2 - Information Theory, IEEE Transactions on SP - 1307 KW - bounds KW - information KW - risk KW - theory AU - Zhang, Tong PY - 2006/04/03/ UR - http://dx.doi.org/10.1109/TIT.2005.864439 ER -