Improved Convergence Rate of Nested Simulation with LSE on Sieve
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916689539497984 |
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| author | Liu, Ruoxue Ding, Liang Wang, Wenjia Zou, Lu |
| author_facet | Liu, Ruoxue Ding, Liang Wang, Wenjia Zou, Lu |
| contents | Nested simulation encompasses the estimation of functionals linked to conditional expectations through simulation techniques. In this paper, we treat conditional expectation as a function of the multidimensional conditioning variable and provide asymptotic analyses of general Least Squared Estimators on sieve, without imposing specific assumptions on the function's form. Our study explores scenarios in which the convergence rate surpasses that of the standard Monte Carlo method and the one recently proposed based on kernel ridge regression. We also delve into the conditions that allow for achieving the best possible square root convergence rate among all methods. Numerical experiments are conducted to support our statements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11756 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved Convergence Rate of Nested Simulation with LSE on Sieve Liu, Ruoxue Ding, Liang Wang, Wenjia Zou, Lu Statistics Theory Nested simulation encompasses the estimation of functionals linked to conditional expectations through simulation techniques. In this paper, we treat conditional expectation as a function of the multidimensional conditioning variable and provide asymptotic analyses of general Least Squared Estimators on sieve, without imposing specific assumptions on the function's form. Our study explores scenarios in which the convergence rate surpasses that of the standard Monte Carlo method and the one recently proposed based on kernel ridge regression. We also delve into the conditions that allow for achieving the best possible square root convergence rate among all methods. Numerical experiments are conducted to support our statements. |
| title | Improved Convergence Rate of Nested Simulation with LSE on Sieve |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2310.11756 |