This paper investigates Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, best linear unbiased predictor for two cases is considered, according to whether there noise at target or not. We show that mean squared prediction error converges a nonzero constant if location, and we provide an upper bound of no location. investigate use stochastic Krig...

The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of uncertainty of EBLUP is the estimation of the mean squared error (MSE) and the confidence interval, which h...

This article presents a new investigation to the linear mixed model y = Xβ + Zγ + ε with fixed effect Xβ and random effect Zγ under a general assumption via some novel algebraic tools in matrix theory, and reveals a variety of deep and profound properties hidden behind the linear mixed model. We first derive exact formulas for calculating the best linear unbiased predictor (BLUP) of a general v...