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Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling

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  • van Waaij, Jan
  • van Zanten, Harry

Abstract

We study random series priors for estimating a functional parameter f∈L2[0,1]. We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve posterior contraction at optimal rates and adaptation to arbitrary degrees of smoothness. We present general results that can be combined with existing rate of contraction results for various nonparametric estimation problems. We give concrete examples for signal estimation in white noise and drift estimation for a one-dimensional SDE.

Suggested Citation

  • van Waaij, Jan & van Zanten, Harry, 2017. "Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 93-99.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:93-99
    DOI: 10.1016/j.spl.2016.12.009
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    References listed on IDEAS

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    1. van der Meulen, Frank & Schauer, Moritz & van Zanten, Harry, 2014. "Reversible jump MCMC for nonparametric drift estimation for diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 615-632.
    2. repec:dau:papers:123456789/11426 is not listed on IDEAS
    3. repec:dau:papers:123456789/7335 is not listed on IDEAS
    4. Weining Shen & Subhashis Ghosal, 2015. "Adaptive Bayesian Procedures Using Random Series Priors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1194-1213, December.
    5. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve Prior," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 549-570, September.
    6. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve prior," Working Papers 2013-19, Center for Research in Economics and Statistics.
    Full references (including those not matched with items on IDEAS)

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