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• W2963503003 abstract "We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable Banach space. We derive the optimum convergence rate for the kernel estimate of the parameter in this setup. The small ball probability in the covariate space plays a critical role in determining the asymptotic variance of kernel estimates. Unlike the case of finite-dimensional covariates, we show that the asymptotic orders of the bias and the variance of the estimate achieving the optimum convergence rate may be different for infinite-dimensional covariates. Also, the bandwidth, which balances the bias and the variance, may lead to an estimate with suboptimal mean square error for infinite-dimensional covariates. We describe a data-driven adaptive choice of the bandwidth and derive the asymptotic behavior of the adaptive estimate." @default.
• W2963503003 created "2019-07-30" @default.
• W2963503003 creator A5031272641 @default.
• W2963503003 creator A5090577298 @default.
• W2963503003 date "2018-11-17" @default.
• W2963503003 modified "2023-09-25" @default.
• W2963503003 title "Convergence rates for kernel regression in infinite-dimensional spaces" @default.
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• W2963503003 doi "https://doi.org/10.1007/s10463-018-0697-2" @default.
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