Optimal Estimation of A Quadratic Functional and Detection of Simultaneous Signals

Autor:	Cai, T. Tony, Tan, Xin Lu
Rok vydání:	2015
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	Motivated by applications in genomics, this paper studies the problem of optimal estimation of a quadratic functional of two normal mean vectors, $Q(\mu, \theta) = \frac{1}{n}\sum_{i=1}^n\mu_i^2\theta_i^2$, with a particular focus on the case where both mean vectors are sparse. We propose optimal estimators of $Q(\mu, \theta)$ for different regimes and establish the minimax rates of convergence over a family of parameter spaces. The optimal rates exhibit interesting phase transitions in this family. The simultaneous signal detection problem is also considered under the minimax framework. It is shown that the proposed estimators for $Q(\mu, \theta)$ naturally lead to optimal testing procedures. Comment: 41 pages including appendix, 3 figures, 3 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1505.01585 Zobrazit plný text záznamu View this record from Arxiv