摘要
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.
作者
王珊珊
丁浩
王占锋
Shanshan Wang;Hao Ding;Zhanfeng Wang(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China)
基金
supported in part by the National Natural Science Foundation of China (11971457)
Anhui Provincial Natural Science Foundation (1908085MA06)
the Fundamental Research Funds for the Central Universities(WK2040000035)。
关键词
拓展的t过程回归
非线性随机效应
协方差核函数
稳健
extended t-process regression
nonlinear random effects
covariance kernel function
robustness