Minimax Risk for Missing Mass Estimation

Nikhilesh Rajaraman; Andrew Thangaraj; Ananda Theertha Suresh

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arXiv · 1705.05006

Minimax Risk for Missing Mass Estimation

Nikhilesh Rajaraman·Andrew Thangaraj·Ananda Theertha Suresh

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Abstract

The problem of estimating the missing mass or total probability of unseen elements in a sequence of $n$ random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to be between $0.6080/n$ and $0.6179/n$. The minimax risk is shown to be lower bounded by $0.25/n$. This appears to be the first such published result on minimax risk for estimation of missing mass, which has several practical and theoretical applications.

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Nikhilesh Rajaraman, Andrew Thangaraj, Ananda Theertha Suresh. 2017-05-14. Minimax Risk for Missing Mass Estimation. https://arxiv.org/abs/1705.05006

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