| Autor: |
Chopin, Nicolas, Crucinio, Francesca R., Singh, Sumeetpal S. |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of $f$ and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters -- which depend on $m$ -- automatically, with a view to make the whole approach simple to use. We develop our methods for the specific functions $f(x)=\log x$ and $f(x)=1/x$, as they arise in several statistical applications such as maximum likelihood estimation of latent variable models and Bayesian inference for un-normalised models. Detailed numerical studies are performed for a range of applications to determine how competitive and reliable the proposed approach is. |
| Databáze: |
arXiv |
| Externí odkaz: |
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