Local limit theorems and strong approximations for Robbins-Monro procedures
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit theorems approximate the stochastic performance of the algorithm. Here, we...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
[01 Oct 2025]
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| In: |
Statistics
Year: 2025, Pages: 1-37 |
| ISSN: | 1029-4910 |
| DOI: | 10.1080/02331888.2025.2562301 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1080/02331888.2025.2562301
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| Author Notes: | Valentin Konakov, Enno Mammen & Lorick Huang |
| Summary: | The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit theorems approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for getting them are local limit theorems, that is, studying the convergence of the density of the algorithm. The analysis relies on a version of parametrix techniques for Markov chains converging to diffusions. The main difficulty that arises here is the fact that the drift is unbounded. |
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| Item Description: | Gesehen am 30.01.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1029-4910 |
| DOI: | 10.1080/02331888.2025.2562301 |