Maximal Ancillarity, Semiparametric Efficiency, and the Elimination of Nuisances
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arXiv
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| Natura: | Preprint |
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2026
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| author | Hallin, Marc Werker, Bas J. M. Zhou, Bo |
| author_facet | Hallin, Marc Werker, Bas J. M. Zhou, Bo |
| contents | Restricting statistical experiments via nuisance-ancillary $σ$-fields yields nuisance-free experiments. However, a moot point with ancillarity is that maximal ancillary $σ$-fields are typically not unique. There are exceptions, though, among which the limiting experiments in a locally asymptotically normal (LAN) context. Building on this, we address the maximal ancillarity uniqueness problem by adopting a Hájek-Le Cam asymptotic perspective and define the concept of sequences of locally asymptotically maximal nuisance-ancillary $σ$-fields. We then show that any semiparametrically efficient procedure admits versions that are measurable with respect to such $σ$-fields while enjoying strict finite-sample nuisance-ancillarity, hence eliminating the nuisance without the hassle of estimating it. This is in sharp contrast with classical tangent space projections, which also achieve semiparametric efficiency but only enjoy asymptotic nuisance-ancillarity -- at the price, moreover, of adequately estimating the nuisance. When the nuisance is the density of some noise or innovation driving the data-generating process of a LAN experiment, we show that a sequence of locally asymptotically maximal nuisance-ancillary $σ$-fields is generated by the so-called center-outward residual ranks and signs based on measure transportation results. Restricting local experiments to such $σ$-fields yields sequences of finite-sample nuisance-free (here, distribution-free) restrictions of the original local LAN experiments that nevertheless achieve the semiparametric efficiency bounds of the original ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal Ancillarity, Semiparametric Efficiency, and the Elimination of Nuisances Hallin, Marc Werker, Bas J. M. Zhou, Bo Statistics Theory 62G10, 62G20, 62P20, 62M10 Restricting statistical experiments via nuisance-ancillary $σ$-fields yields nuisance-free experiments. However, a moot point with ancillarity is that maximal ancillary $σ$-fields are typically not unique. There are exceptions, though, among which the limiting experiments in a locally asymptotically normal (LAN) context. Building on this, we address the maximal ancillarity uniqueness problem by adopting a Hájek-Le Cam asymptotic perspective and define the concept of sequences of locally asymptotically maximal nuisance-ancillary $σ$-fields. We then show that any semiparametrically efficient procedure admits versions that are measurable with respect to such $σ$-fields while enjoying strict finite-sample nuisance-ancillarity, hence eliminating the nuisance without the hassle of estimating it. This is in sharp contrast with classical tangent space projections, which also achieve semiparametric efficiency but only enjoy asymptotic nuisance-ancillarity -- at the price, moreover, of adequately estimating the nuisance. When the nuisance is the density of some noise or innovation driving the data-generating process of a LAN experiment, we show that a sequence of locally asymptotically maximal nuisance-ancillary $σ$-fields is generated by the so-called center-outward residual ranks and signs based on measure transportation results. Restricting local experiments to such $σ$-fields yields sequences of finite-sample nuisance-free (here, distribution-free) restrictions of the original local LAN experiments that nevertheless achieve the semiparametric efficiency bounds of the original ones. |
| title | Maximal Ancillarity, Semiparametric Efficiency, and the Elimination of Nuisances |
| topic | Statistics Theory 62G10, 62G20, 62P20, 62M10 |
| url | https://arxiv.org/abs/2603.07273 |