Joint parsimonious modeling the mean and covariance is important for analyzing longitudinal data, because it accounts for the efficiency of parameter estimation and easy interpretation of variability. The main potential risk is that it may lead to inefficient or biased estimators of parameters while misspecification occurs. A good alternative is the semiparametric model. In this paper, a Bayesian approach is proposed for modeling the mean and covariance simultaneously by using semiparametric models and the modified Cholesky decomposition. We use a generalized prior to avoid the knots selection while using B-spline to approximate the nonlinear part and propose a Markov Chain Monte Carlo scheme based on Metropolis–Hastings algorithm for computations. Simulation studies and real data analysis show that the proposed approach yields highly efficient estimators for the parameters and nonparametric parts in the mean, meanwhile providing parsimonious estimation for the covariance structure.

中文翻译：

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纵向数据的贝叶斯联合半参数均值-协方差建模

均值和协方差联合简约建模对于分析纵向数据很重要，因为它考虑了参数估计的效率和易变性的解释。主要的潜在风险是，当发生错误指定时，它可能导致参数估计器的效率低下或带有偏见。半参数模型是一个很好的选择。本文提出了一种贝叶斯方法，通过使用半参数模型和改进的Cholesky分解同时对均值和协方差建模。在使用B样条近似非线性部分时，我们使用广义先验来避免打结，并提出了基于Metropolis-Hastings算法的马尔可夫链蒙特卡罗方案进行计算。