Density estimation from batched broken random samples
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912894524850176 |
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| author | Bi, Hancheng Schmitzer, Bernhard Stier, Thilo D. |
| author_facet | Bi, Hancheng Schmitzer, Bernhard Stier, Thilo D. |
| contents | The broken random sample problem was first introduced by DeGroot, Feder, and Gole (1971, Ann. Math. Statist.): in each observation (batch), a random sample of $M$ i.i.d. point pairs $ ((X_i,Y_i))_{i=1}^M$ is drawn from a joint distribution with density $p(x,y)$, but we can observe only the unordered multisets $(X_i)_{i=1}^M$ and $(Y_i)_{i=1}^M$ separately; that is, the pairing information is lost. For large $M$, inferring $p$ from a single observation has been shown to be essentially impossible. In this paper, we propose a parametric method based on a pseudo-log-likelihood to estimate $p$ from $N$ i.i.d. broken sample batches, and we prove a fast convergence rate in $N$ for our estimator that is uniform in $M$, under mild assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Density estimation from batched broken random samples Bi, Hancheng Schmitzer, Bernhard Stier, Thilo D. Statistics Theory 62E17 (Primary), 60G70, 62F10 The broken random sample problem was first introduced by DeGroot, Feder, and Gole (1971, Ann. Math. Statist.): in each observation (batch), a random sample of $M$ i.i.d. point pairs $ ((X_i,Y_i))_{i=1}^M$ is drawn from a joint distribution with density $p(x,y)$, but we can observe only the unordered multisets $(X_i)_{i=1}^M$ and $(Y_i)_{i=1}^M$ separately; that is, the pairing information is lost. For large $M$, inferring $p$ from a single observation has been shown to be essentially impossible. In this paper, we propose a parametric method based on a pseudo-log-likelihood to estimate $p$ from $N$ i.i.d. broken sample batches, and we prove a fast convergence rate in $N$ for our estimator that is uniform in $M$, under mild assumptions. |
| title | Density estimation from batched broken random samples |
| topic | Statistics Theory 62E17 (Primary), 60G70, 62F10 |
| url | https://arxiv.org/abs/2602.09833 |