Confidence bands for inverse regression models with application to gel electrophoresis

M. Birke, N. Bissantz, H. Holzmann
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引用次数: 2

Abstract

We construct uniform confidence bands for the regression function in inverse, homoscedastic regression models with convolution-type operators. Here, the convolution is between two non-periodic functions on the whole real line rather than between two period functions on a compact interval, since the former situation arguably arises more often in applications. First, following Bickel and Rosenblatt [Ann. Statist. 1, 10711095] we construct asymptotic confidence bands which are based on strong approximations and on a limit theorem for the supremum of a stationary Gaussian process. Further, we propose bootstrap confidence bands based on the residual bootstrap. A simulation study shows that the bootstrap confidence bands perform reasonably well for moderate sample sizes. Finally, we apply our method to data from a gel electrophoresis experiment with genetically engineered neuronal receptor subunits incubated with rat brain extract.
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应用于凝胶电泳的逆回归模型置信带
我们构造了具有卷积型算子的逆、同方差回归模型中回归函数的一致置信带。这里,卷积是在整条实线上的两个非周期函数之间进行的,而不是在紧化区间上的两个周期函数之间进行的,因为前一种情况在应用中可能会更频繁地出现。首先,遵循Bickel和Rosenblatt [Ann。我们构造了一个基于强近似和一个平稳高斯过程的极限定理的渐近置信带。进一步,我们提出了基于残差自举的自举置信带。仿真研究表明,自举置信带在中等样本量下表现相当好。最后,我们将我们的方法应用于与大鼠脑提取物孵育的基因工程神经元受体亚基的凝胶电泳实验数据。
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