Some Alternatives to the Box-Cox Regression Model

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Abstract
A nonlinear regression model is proposed as an alternative to the Box-Cox regression model for nonnegative variables. The functional form contains linear, exponential, and reciprocal models as special cases. Unlike Box-Cox type approaches, the proposed estimators of the conditional mean function are robust to conditional variance and other distributional misspecifications. Computationally simple, robust Lagrange multiplier statistics for restricted versions of the model are derived. Scale invariant t-statistics are proposed, and the Lagrange multiplier statistic for exclusion restrictions is shown to be scale invariant.