论文标题
指数家族回归的非DATA拆分估计器选择
Non-Data-Splitting Estimator Selection for Regression in Exponential Families
论文作者
论文摘要
我们观察$ n $独立的随机变量对$（w_ {i}，y_ {i}）$，其中$ y_ {i} $的条件分布给定的$ w_ {i} = w_ {i} = w_ {i} $遵循一个单参数级的expentient expentient expentient expentient expentential家族，带有参数$ \ \ bsg^{$} $} $};我们的目标是估计回归函数$ \ bsg^{*} $。我们从基于我们的观察值的分段常数候选估计器的任意集合开始，并使用相同的数据从此集合中选择一个估算器。我们的方法对候选估计量对数据的依赖性不可知，与数据拆分，交叉验证和固定等方法不同。为了证明其理论性能，我们为选定的估计量提供了非肿瘤风险。然后，我们解释了如何应用程序以更改指数家庭中的检测。通过在不同方案和实际数据集中的比较模拟研究中说明了拟议方法的实际性能。
We observe $n$ independent pairs of random variables $(W_{i}, Y_{i})$, where the conditional distribution of $Y_{i}$ given $W_{i}=w_{i}$ follows a one-parameter exponential family with parameter $\bsg^{*}(w_{i})\in\R$. Our goal is to estimate the regression function $\bsg^{*}$. We start with an arbitrary collection of piecewise constant candidate estimators based on our observations and, using the same data, select an estimator from this collection. Our approach is agnostic to the dependencies of the candidate estimators on the data, differing from methods like data splitting, cross-validation, and hold-out. To demonstrate its theoretical performance, we provide a non-asymptotic risk bound for the selected estimator. We then explain how to apply the procedure to changepoint detection in exponential families. The practical performance of the proposed approach is illustrated through a comparative simulation study under different scenarios and real datasets.
