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One-step estimation for varying coefficients models with unknown functions of different degrees of smoothness. (Chinese. English summary) Zbl 1174.62367

Summary: An one-step estimation method is proposed to estimate all the unknown functions in varying coefficients models, where the degrees of smoothness may be different from each other. In the one-step estimation approach, the local estimators of all the unknown functions and their derivatives can be obtained by only one minimization operation. The asymptotic properties of the estimators, including bias, variance and asymptotic distributions, are derived. It is shown that all the one-step estimators achieve the optimal convergence rates.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
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