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局部最大似然估计与推断AI 解读

Summary Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local…

局部多项式拟合的数据驱动带宽选择：可变带宽与空间适应AI 解读

SUMMARY When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important issue of how to select the smoothing parameter or bandwidth. In the case of estimating curves with a complicated structure, a variable bandwidth is desirable. Furthermore, the bandwidth should be indicated by the data themselves. Recent developments in nonparametric smoothing…

可变带宽与局部线性回归平滑器AI 解读

In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable…

Kaplan–Meier 估计量一类泛函的几乎必然渐近表示AI 解读

This paper deals with censored data estimation of a general class of von Mises-type functionals of the survival time distribution $F$. Conditions are given under which an almost sure asymptotic representation holds for the estimator, obtained by applying the same functional to $\hat{F}_n$, the product-limit estimator of Kaplan and Meier.