TY - GEN
T1 - Minimax estimation of the L1 distance
AU - Jiao, Jiantao
AU - Han, Yanjun
AU - Weissman, Tsachy
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - We consider the problem of estimating the L1 distance between two discrete probability measures P and Q from empirical data in a nonasymptotic and large alphabet setting. We construct minimax rate-optimal estimators for L1(P,Q) when Q is either known or unknown, and show that the performance of the optimal estimators with n samples is essentially that of the Maximum Likelihood Estimators (MLE) with n ln n samples. Hence, we demonstrate that the effective sample size enlargement phenomenon, discovered and discussed in Jiao et al. (2015), holds for this problem as well. However, the construction of optimal estimators for L1(P,Q) requires new techniques and insights outside the scope of the Approximation methodology of functional estimation in Jiao et al. (2015).
AB - We consider the problem of estimating the L1 distance between two discrete probability measures P and Q from empirical data in a nonasymptotic and large alphabet setting. We construct minimax rate-optimal estimators for L1(P,Q) when Q is either known or unknown, and show that the performance of the optimal estimators with n samples is essentially that of the Maximum Likelihood Estimators (MLE) with n ln n samples. Hence, we demonstrate that the effective sample size enlargement phenomenon, discovered and discussed in Jiao et al. (2015), holds for this problem as well. However, the construction of optimal estimators for L1(P,Q) requires new techniques and insights outside the scope of the Approximation methodology of functional estimation in Jiao et al. (2015).
UR - http://www.scopus.com/inward/record.url?scp=84985993094&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84985993094&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2016.7541399
DO - 10.1109/ISIT.2016.7541399
M3 - Conference contribution
AN - SCOPUS:84985993094
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 750
EP - 754
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -