弱相关模型中的分块拟回归

Blockwise Quasi- regression in Models with Weakly Dependent Processes

为了减少计算复杂性，在计算机试验设计中，最近人们提出了一种新的统计方法－拟回归（Owen(2000),An and Owen(2001),在独立同分布模型中，拟回归不仅能提高计算速度，而且在较好的统计性质，然而，对相关数据模型，这种方法的统计性质并不好，针对这一问题，在不增加计算复杂性的条件下，本文提出一种分块拟回归方法。我们研究分块拟回归的小样本和大样本性质，如无偏性，均方收敛性，强收敛性和渐近正态性。结果表明分块拟回归比原拟回归渐近有效，本文还讨论了曲线拟合的性质，指出了分块拟回归（包括原拟回归）在高维问题中的缺陷，为改善曲线拟合，我们还提出一种修正分拟回归，研究表明，在高维问题中，修正分块似回归是十分有效的。

Quasi-regression,a new method motivated by the problems arising in computer experiments ,mainly focuses on speeding up evaluation (Owen(2000),An and Owen(2001)).It is valid not only in speeding up evaluation,but also in parametric statistical inference for independent processes.However,it is invalid for dependent observations,so, we introduce blockwise quasi-regression for dependent processes under the condition in which the cost for calculation is not increased,for this method,some small sample and large sample superiority,for example,the unbiasedness,convergence,asymptotic normality are discussed.The results show this method is more asymptotically efficient than the original quasi-regression.We also find some defects of quasi-in high dimension models. To improve the quasi-regression, we construct a corrected quasi-regression.The results show this corrected quasi-regression is more efficient than original quasi-regression in high dimension model.