带有非参随机效应的稳健函数型回归模型

Robust function-on-function regression model with nonparametric random effects

拓展的t过程对异常值稳健并且拥有高斯过程很多优良的性质。为此利用拓展的t过程先验提出了一个带有非参数随机效应的函数型模型,并在模型里考虑了个体效应的异质性、灵活的均值函数、非参协方差函数和稳健性。并进一步提出了基于似然的估计方法,给出了参数估计的信息相合性,最后通过模拟研究和实际数据分析来验证所提的方法。

Extended t-process is robust to outliers and inherits many attractive properties from the Gaussian process. In this paper, we provide a function-on-function nonparametric random-effects model using extended t-process priors in which we consider heterogeneity of individual effect, flexible mean function, nonparametric covariance function and robustness. A likelihood-based estimation procedure is constructed to estimate parameters involved in the model. Information consistency for the parameter estimation is provided. Simulation studies and a real data example are further investigated to evaluate the performance of the developed procedures.