Mathematical Sciences: Adaptive estimation of nonparametric curves

本研究探讨了适应性风险的急剧收敛 无先验非参数曲线的估计 由于最优风险收敛 在这种情况下，关键取决于 估计曲线，目标是开发一个合适的估计器 而不需要平滑度的先验知识。 特定领域 概率密度估计、非参数估计 回归、滤波和谱密度估计。 大多数（最佳）数据曲线估计依赖于 关于要估计的曲线的平滑度的假设。 自适应估计允许关于平滑度的信息被 数据（data）是指数据（data）。 这是在 同时，作为估计曲线的过程的一部分， 本身 对于这种顺序方法，数据量 要求（样本量）取决于观察结果和 基本曲线 这两种理论方法都可以实现 我们会考虑整体策略和一些应用。

This research examines sharp risk convergence for adaptive estimates of nonparametric curves in the absence of prior information on nuisance parameters.Since optimal risk convergence in this context depends crucially on the smoothness of the estimated curve, the goal is to develop a suitable estimator without a priori knowledge of the smoothness. Particular areas of application are probability density estimation, nonparametric regression, filtering and spectral density estimation. Most (optimal) estimates of curves from data rely on assumptions about the smoothness of the curve to be estimated. Adaptive estimation allows information about the smoothness to be built up as observations (data) are gathered. This is done at the same time and as part of the process of estimating the curve itself. For sequential methods of this kind, the amount of data required (sample size) depends on the observations and the underlying curve. Both theoretical approaches to an optimal overall strategy and some applications will be considered.