کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5129347 1489645 2017 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Simultaneous confidence bands for contrasts between several nonlinear regression curves
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Simultaneous confidence bands for contrasts between several nonlinear regression curves
چکیده انگلیسی

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 Naiman's inequality for Gaussian random processes. As an illustrative example, growth curves of consomic mice are analyzed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 155, March 2017, Pages 83-104
نویسندگان
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