Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation
Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation
复制标题
多参数弱收敛在自适应非参数曲线估计中的应用
DOI：
10.1007/978-94-011-3222-0_11
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Kathy Prewitt
中科院分区：
文献类型：
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作者：
H. Müller;Kathy Prewitt
我们概述了随机过程的弱收敛在通过有效的基于数据的局部带宽选择来获得自适应非参数曲线估计器方面的应用。指出了基于多元时间随机过程的新发展。例如，多变量曲线估计，其中为不同的坐标选择几个局部带宽，以及曲线的局部泛函的估计，其可以表示为局部偏差过程的最大值或零点，并且也取决于带宽。作为例证，我们证明了概率密度函数的自适应模式估计是二维过程在带宽和偏差坐标上弱收敛的结果。讨论了各种自适应模式估计器。
We give an overview on applications of weak convergence of stochastic processes to obtain adaptive nonparametric curve estimators through efficient data-based local bandwidth choices. We point out new developments based on multivariate time stochastic processes. Examples are multivariate curve estimates, where several local bandwidths are to be chosen for different coordinates, and estimates of local functionals of curves which can be expressed as maxima or zeros of local deviation processes and also depend on a bandwidth. As an illustration, we show that adaptive mode estimation for a probability density function is a consequence of weak convergence of a two-dimensional process in a bandwidth and a deviation coordinate. Various adaptive mode estimators are discussed.