主 题:Simultaneous confidence bands for contrasts between several nonlinear regression curves
内容简介:We propose simultaneous confidence bands of the hyperbolic-type for the contrasts between several nonlinear (curvilinear) regression curves. The critical value of a confidence band is determined from the distribution of the maximum of a chi-square random process defined on the domain of explanatory variables. We use the volume-of-tube method to derive an upper tail probability formula of the maximum of a chi-square random process, which is asymptotically exact and sufficiently accurate in commonly used tail regions. Moreover, we prove that the formula obtained is equivalent to the expectation of the Euler–Poincaré characteristic of the excursion set of the chi-square random process, and hence conservative. This result is therefore a generalization of Naman’s inequality for Gaussian random processes. As an illustrative example, growth curves of consomic mice are analyzed.
报告人:陆小磊 博士
时 间:2019-01-04 15:00
地 点:竞慧东楼302
举办单位:统计与数学学院 澄园书院
