双幂变换下正态线性回归模型参数的假设检验

Hypothesis Testing for Parameters in Normal Linear Regression Model Under Dual Power Transformation

假设检验是统计推断的一种形式。文章主要针对双幂变换下正态线性回归模型中的变换参数的假设检验问题进行研究。构造关于变换参数的F分布统计量,并在此基础上构造变换参数在一定置信水平下的置信域,通过大量模拟研究表明了该置信域为一区间。检验功效是衡量假设检验的检验效果的一个重要指标。为此,给出了检验的功效函数,通过大量模拟显示功效函数大小与方差真实值取值有关系,方差取值越小,功效函数越不稳定。

Hypothesis testing is form of statistical inference. The article is primarily for the study of hypothesis testing for pa- rameters in normal linear regression model under dual power transformation. We construct the statistics of F distribution for pa- rameters. And on this basis we construct the confidence interval for parameter under certain confidence level, then many simula- tions show the confidence interval is an interval. Power of the test is an important indicator of the measurement of the effect of the hypothesis testing. Therefore, Given the power function, many simulation studies show that the power function has relation with the value of variance, that is, the smaller the variance, the less stable the power function.