Wang Lan, Zhou Xiao-Hua
School of Statistics, University of Minnesota, 224 Church Street SE, Minneapolis, Minnesota 55455, USA.
Biometrics. 2007 Dec;63(4):1218-25. doi: 10.1111/j.1541-0420.2007.00805.x. Epub 2007 May 2.
Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is shown that the test statistic has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives. We suggest a simple bootstrap algorithm to approximate the distribution of the test statistic in finite sample size. Numerical simulations demonstrate the satisfactory performance of the proposed test. We also illustrate the application by the analysis of a radioimmunoassay data set.
异方差数据在许多应用中都会出现。在异方差回归分析中，方差通常被建模为协变量或回归均值的参数函数。我们提出一种核平滑型非参数检验，用于检验给定参数方差结构的适当性。该检验无需为随机误差指定参数分布。结果表明，在原假设下检验统计量具有渐近正态分布，并且对一大类备择假设具有强大的检验能力。我们建议一种简单的自助算法来近似有限样本量下检验统计量的分布。数值模拟证明了所提出检验的良好性能。我们还通过对一个放射免疫分析数据集的分析来说明该检验的应用。
