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Minimax theory of nonparametric hazard rate estimation: efficiency and adaptation

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  • Sam Efromovich

Abstract

The problem of nonparametric estimation of the hazard rate function is considered and the theory of sharp minimax estimation for two global and two local Sobolev classes is developed. Several interesting outcomes are as follows: (i) Classical global and local function classes imply different sharp constants of the MISE convergence. This is in contrary to the density estimation where sharp constants are the same. (ii) Two global classes imply different sharp constants and correspondingly require using different linear estimates. (iii) Two local classes imply the same sharp constant, and nonetheless require different linear estimates to attain this constant. (iv) A sharp-minimax data-driven estimator is proposed that adapts to the smoothness of the hazard rate and to an unknown underlying function class, and it is tested for small samples via a numerical study. Copyright The Institute of Statistical Mathematics, Tokyo 2016

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  • Sam Efromovich, 2016. "Minimax theory of nonparametric hazard rate estimation: efficiency and adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 25-75, February.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:1:p:25-75
    DOI: 10.1007/s10463-014-0487-4
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    1. A. Antoniadis & G. Grégoire & G. Nason, 1999. "Density and hazard rate estimation for right‐censored data by using wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 63-84.
    2. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
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    1. Sam Efromovich & Jufen Chu, 2018. "Hazard rate estimation for left truncated and right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 889-917, August.

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