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<p>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 nonparametric 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 use kernel ridge regression with inducing points and neural networks as examples to illustrate our theorems. Numerical experiments are conducted to support our statements.</p>

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Improved Convergence Rate of Nested Simulation with LSE on Sieve

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Ruo-xue Liu,
  • Liang Ding,
  • Wen-jia Wang,
  • Lu Zou

摘要

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 nonparametric 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 use kernel ridge regression with inducing points and neural networks as examples to illustrate our theorems. Numerical experiments are conducted to support our statements.