Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918461217701888 |
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| author | Hjort, Nils Lid |
| author_facet | Hjort, Nils Lid |
| contents | This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model. We look at cases where the nonparametric part of the construction is a Dirichlet process or relatives thereof. (2) Express the density as an additive expansion of orthogonal basis functions, and place priors on the coefficients. Here attention is given to a certain robust Hermite expansion around the normal distribution. Multiplicative expansions are also considered. (3) Express the unknown density as locally being of a certain parametric form, then construct suitable local likelihood functions to express information content, and place local priors on the local parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20238 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants] Hjort, Nils Lid Statistics Theory This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model. We look at cases where the nonparametric part of the construction is a Dirichlet process or relatives thereof. (2) Express the density as an additive expansion of orthogonal basis functions, and place priors on the coefficients. Here attention is given to a certain robust Hermite expansion around the normal distribution. Multiplicative expansions are also considered. (3) Express the unknown density as locally being of a certain parametric form, then construct suitable local likelihood functions to express information content, and place local priors on the local parameters. |
| title | Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants] |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2604.20238 |