Kenta Takatsu, Arun Kumar Kuchibhotla
arXiv 14 Jan 2025 · Mathematics — Statistics Theory
arXiv:2501.07772 · PDF · DOI · OpenAlex · Extracted main text
This manuscript studies a general approach to construct confidence sets for the solution of population-level optimization, commonly referred to as M-estimation. Statistical inference for M-estimation poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. Moreover, we provide a comprehensive width analysis of the proposed confidence set, showing that the convergence rate of the diameter is adaptive to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems.
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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 | van der Vaart, A. and Wellner, J. A (1996) Weak convergence and empirical processes | 1.000 | 9 | 4 | 100% |
| 2 | Robins, J. and van der Vaart, A (2006) Adaptive nonparametric confidence sets | 1.000 | 8 | 3 | 100% |
| 3 | Kim, I. and Ramdas, A (2024) Dimension-agnostic inference using cross u-statistics | 1.000 | 6 | 3 | 100% |
| 4 | Kim, J. and Pollard, D (1990) Cube root asymptotics | 0.928 | 4 | 4 | 100% |
| 5 | Ledoux, M. and Talagrand, M (2013) Probability in Banach Spaces: isoperimetry and processes | 0.928 | 4 | 3 | 100% |
| 6 | Giné, E. and Nickl, R (2021) Mathematical foundations of infinite-dimensional statistical models | 0.843 | 3 | 3 | 100% |
| 7 | Knight, K (1998) Limiting distributions for l 1 regression estimators under general conditions | 0.811 | 4 | 2 | 100% |
| 8 | Park, B., Balakrishnan, S., and Wasserman, L (2023) Robust universal inference | 0.811 | 4 | 2 | 100% |
| 9 | Vogel, S (2008) Universal confidence sets for solutions of optimization problems | 0.811 | 4 | 2 | 100% |
| 10 | Cattaneo, M. D., Jansson, M., and Nagasawa, K (2020) Bootstrap-based inference for cube root asymptotics | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 101 scored citations.