Andriy Norets, Justinas Pelenis
arXiv 19 Jun 2018 · Mathematics — Statistics Theory · publishedEconometrica (2022) · 4 citations (OpenAlex)
arXiv:1806.07484 · PDF · DOI · OpenAlex · Extracted main text
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total variation distance. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discrete-continuous distributions.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ibragimov, I. A. and R. Z. Hasminskii (1984) More on the estimation of distribution densities | 0.928 | 4 | 3 | 100% |
| 2 | Shen, W., S. T. Tokdar, and S. Ghosal (2013) Adaptive Bayesian multivariate density estimation with Dirichlet mixtures | 0.883 | 16 | 4 | 69% |
| 3 | Tsybakov, A. B (2008) Introduction to Nonparametric Estimation (Springer Series in Statistics) | 0.737 | 4 | 2 | 75% |
| 4 | Hall, P. and D. M. Titterington (1987) On Smoothing Sparse Multinomial Data | 0.644 | 4 | 1 | 100% |
| 5 | Efromovich, S (2011) Nonparametric estimation of the anisotropic probability density of mixed variables | 0.585 | 3 | 1 | 100% |
| 6 | Norets, A. and D. Pati (2017) Adaptive Bayesian Estimation of Conditional Densities self | 0.511 | 4 | 2 | 25% |
| 7 | Ghosal, S. and A. W. van der Vaart (2001) Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities | 0.511 | 3 | 2 | 33% |
| 8 | Ghosal, S. and A. van der Vaart (2007) Posterior convergence rates of Dirichlet mixtures at smooth densities | 0.511 | 3 | 2 | 33% |
| 9 | Ghosal, S., J. K. Ghosh, and A. W. v. d. Vaart (2000) Convergence Rates of Posterior Distributions | 0.511 | 2 | 2 | 50% |
| 10 | Norets, A. and J. Pelenis (2012) Bayesian modeling of joint and conditional distributions self | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 36 scored citations.