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Janet S. Kim Arnab Maity Raymond J. Carroll David Ruppert 《Journal of computational and graphical statistics》2018,27(1):234-244
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary material for this article is available online. 相似文献
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Analysis of a system of fractional differential equations 总被引:2,自引:0,他引:2
Varsha Daftardar-Gejji A. Babakhani 《Journal of Mathematical Analysis and Applications》2004,293(2):511-522
We prove existence and uniqueness theorems for the initial value problem for the system of fractional differential equations , where Dα denotes standard Riemann-Liouville fractional derivative, 0<α<1, and A is a square matrix. The unique solution to this initial value problem turns out to be , where Eα denotes the Mittag-Leffler function generalized for matrix arguments. Further we analyze the system , , 0<α<1, and investigate dependence of the solutions on the initial conditions. 相似文献
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