Assumption-Lean Honest Inference for $Z$-functionals
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916835159441408 |
|---|---|
| author | Chang, Woonyoung Kuchibhotla, Arun Kumar |
| author_facet | Chang, Woonyoung Kuchibhotla, Arun Kumar |
| contents | We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test inversion principle, enabling honest inference under mild regularity conditions and without explicit variance estimation. To enhance geometric tractability, we propose novel split-normalized and Gateaux-normalized statistics that yield computationally feasible and interpretable confidence sets. A central contribution of this work is a comprehensive non-asymptotic width analysis: we derive high-probability upper bounds on the diameter of the proposed confidence sets, and quantify their proximity to Wald intervals under minimal assumptions. Applications to high-dimensional non-sparse linear and generalized linear regression demonstrate that our procedures achieve valid coverage and near-optimal rate of convergence for the width/diameter, while the classical methods including Wald and bootstrap fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Assumption-Lean Honest Inference for $Z$-functionals Chang, Woonyoung Kuchibhotla, Arun Kumar Statistics Theory We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test inversion principle, enabling honest inference under mild regularity conditions and without explicit variance estimation. To enhance geometric tractability, we propose novel split-normalized and Gateaux-normalized statistics that yield computationally feasible and interpretable confidence sets. A central contribution of this work is a comprehensive non-asymptotic width analysis: we derive high-probability upper bounds on the diameter of the proposed confidence sets, and quantify their proximity to Wald intervals under minimal assumptions. Applications to high-dimensional non-sparse linear and generalized linear regression demonstrate that our procedures achieve valid coverage and near-optimal rate of convergence for the width/diameter, while the classical methods including Wald and bootstrap fail. |
| title | Assumption-Lean Honest Inference for $Z$-functionals |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2407.12278 |