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Adaptive Warped Kernel Estimators

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  • Gaëlle Chagny

Abstract

type="main" xml:id="sjos12109-abs-0001"> In this work, we develop a method of adaptive non-parametric estimation, based on ‘warped’ kernels. The aim is to estimate a real-valued function s from a sample of random couples (X,Y). We deal with transformed data (Φ(X),Y), with Φ a one-to-one function, to build a collection of kernel estimators. The data-driven bandwidth selection is performed with a method inspired by Goldenshluger and Lepski (Ann. Statist., 39, 2011, 1608). The method permits to handle various problems such as additive and multiplicative regression, conditional density estimation, hazard rate estimation based on randomly right-censored data, and cumulative distribution function estimation from current-status data. The interest is threefold. First, the squared-bias/variance trade-off is automatically realized. Next, non-asymptotic risk bounds are derived. Lastly, the estimator is easily computed, thanks to its simple expression: a short simulation study is presented.

Suggested Citation

  • Gaëlle Chagny, 2015. "Adaptive Warped Kernel Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 336-360, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:336-360
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    File URL: http://hdl.handle.net/10.1111/sjos.12109
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    References listed on IDEAS

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    1. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
    2. Shuangge Ma & Michael Kosorok, 2006. "Adaptive penalized M-estimation with current status data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 511-526, September.
    3. Laure Sansonnet, 2014. "Wavelet Thresholding Estimation in a Poissonian Interactions Model with Application to Genomic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 200-226, March.
    4. K. Mehra & Y. Ramakrishnaiah & P. Sashikala, 2000. "Laws of Iterated Logarithm and Related Asymptotics for Estimators of Conditional Density and Mode," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 630-645, December.
    5. Christophe Chesneau, 2007. "A maxiset approach of a Gaussian noise model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 523-546, December.
    6. Lacour, Claire, 2008. "Adaptive estimation of the transition density of a particular hidden Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 787-814, May.
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    Cited by:

    1. Guilloux, Agathe & Lemler, Sarah & Taupin, Marie-Luce, 2016. "Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 141-159.
    2. Gautier, Eric & Gaillac, Christophe, 2019. "Estimates for the SVD of the Truncated Fourier Transform on L2(cosh(b.)) and Stable Analytic Continuation," TSE Working Papers 19-1013, Toulouse School of Economics (TSE).

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