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随设计位置自适应的平滑样条AI 解读

We use a reproducing kernel Hilbert space representation to derive the smoothing spline solution when the smoothness penalty is a function λ(t) of the design space t, thereby allowing the model to adapt to various degrees of smoothness in the structure of the data. We propose a convenient form for the smoothness penalty function and discuss computational algorithms for automatic curve fitting using a generalised crossvalidation measure.

摘要暂缺

摘要暂缺

部分线性模型中的核平滑AI 解读

SUMMARY Kernel smoothing is studied in partial linear models, i.e. semiparametric models of the form yi=ξi′β+f(ti)+εi(1⩽i⩽n), where the ξi are fixed known p vectors, β is an unknown vector parameter and f is a smooth but unknown function. Two methods of estimating β and f are considered, one related to partial smoothing splines and the other motivated by partial residual analysis. Under suitable assumptions, the asymptotic bias and variance are obtained for both methods, and…

样条平滑与非参数回归的最优收敛速率AI 解读

Linear estimation is considered in nonparametric regression models of the form $Y_i = f(x_i) + \varepsilon_i, x_i \in (a, b)$, where the zero mean errors are uncorrelated with common variance $\sigma^2$ and the response function $f$ is assumed only to have a bounded square integrable $q$th derivative. The linear estimator which minimizes the maximum mean squared error summed over the observation points is derived, and the exact minimax rate of convergence is obtained. For…