线性回归模型参数的联立经验Bayes估计的收敛速度

The Convergence Rate of Simultaneous Empirical Bayes Estimator for Parameters in Linear Regression Models

中文摘要:

      本文考虑了线性模型中回归系数β=(β₁,…,β_p)′和误差方差σ²的联立经验Bayes(EB)估计.在二次损失下,利用密度函数及其编导数的核估计构造出参数θ=(β₁,…,β_p,σ²)的联立EB估计,在一定条件下证明了θ的联立EB估计的收敛速度任意接近于1.最后、给出了一个实例.

英文摘要:

      In this paper, the simultaneous empirical Bayes (EB) estimator for regression cofficient β= (β₁,…,β_p)′ and error variance σ² is considered in linear models. Suppose that the loss function is square, the convergence rate of simultaneous EB estimator about the parameter θ=(β₁,…,β_p,σ²) is obtained and this convergence rate can be arbitrarily close to 1 under suitable conditions. At last, an example is given.