长记忆多项式回归模型的置信域估计

Confidence Regions for Polynomial Regression Models

本文主要讨论误差序列存在长记忆性的多项式回归模型的回归参数向量的置信域问题.这是一个涉及到多维空间的问题.我们分别给出了基于普通最小二乘估计(OLS)和广义最小二乘估计(GLS)方法的回归参数的置信域表达式.进一步结合有效样本数的概念,我们对OLS估计的置信域提出了一个改进的方法,并通过计算OLS估计的相对效率度量这种做法给估计精度带来的损失.我们从经验覆盖概率和置信域的体积大小两个方面,对参数的三种置信域估计方法进行比较.Monte Carlo模拟结果显示,在长记忆情况下,改进的方法具有良好的精确度,并且计算量小.

This paper proposes confidence regions for the trend parameters in a linear polynomial regression model with long memory errors. This is a problem related to multi- dimensional space. We establish two kinds of confidence regions for the trend parameters based on the Ordinary Least Square Estimates （OLS） and the Generalized Least Squares Estimates （GLS）. Then, we construct a calibrated confidence region, based on the concept of effective sample sizes. We measure the loss by the relative efficiency. Through a Monte Carlo simulation study, we do a comparison among the three methods of confidence regions in empirical coverage probabilities and the volume. The result shows that the advantages of our calibrated confidence regions lie in its good performance and easy computation.