Some Alternatives to the Box-Cox Regression Model
提出一种替代Box-Cox模型的非线性回归形式，适用于非负因变量，能包含线性、指数、常弹性等常见设定，且参数易解释。估计方法对条件方差误设稳健，并推导了拉格朗日乘子检验。
A nonlinear regression model is proposed as an alternative to the Box-Cox regression model for nonnegative variables.The functional form contains as special cases the linear, exponential, constant elasticity, and generalized CES specifications, as well as other functional forms used by applied econometricians .The model can be derived from but is more general than a particular modification of the Box-Cox model.Because the model is specified directly in terms of E(y|x), the parameters are easy to interpet and economic quantities are straightforward to compute.Unlike Box-Cox type approaches, the proposed weighted nonlinear least squares estimators of the conditional mean function are robust to conditional variance and other distributional misspecif ications ; in some leading cases they are also asymptotically efficient.Computationally simple, robust lagrange multiplier statistics for various restricted versions of the model are derived.The explained variable can be continuous, discrete, or some combination of the two.A method for obtaining scale-invariant t-statistics is also discussed, while the lagrange multiplier test for exclusion restrictions is shown to be scale invariant.