Variance Estimates in Models with the Box-Cox Transformation: Implications for Estimation and Hypothesis Testing
解析了含Box-Cox变换模型中参数估计的方差-协方差矩阵，解释了不同估计算法的效率差异、OLS和梯度法估计系数方差的偏差原因，以及t统计量缺乏尺度不变性导致假设检验误导的问题。
The variance-covariance matrix of the parameter estimates in a model containing the Box-Cox transformation is analytically examined. Breaking the variance-covariance matrix into components helps in understanding (1) why some estimation algorithms are more efficient than others, (2) why both iterated OLS estimation and first derivative-only gradient estimation methods obtain biased estimates of the variances of the coefficients (with OLS underestimating the variances, and first derivative methods overestimating them), and (3) how the lack of scale invariance in the t-ratios for the linear coefficients makes hypothesis testing very misleading.