Artificial linear regressions often provide a convenient way to calculate test statistics and estimate covariance matrices. This paper discusses one family of these regressions, called "double-length" because the number of observations in the artificial regression is twice the actual number of...

Associated with every popular nonlinear estimation method is at least one "artificial" linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses,...

We propose a family of transformations which, unlike the Box-Cox transformation, can sensibly be applied to variables of either sign which may be near or far from zero. We derive two forms of Lagrange multiplier test for the null hypothesis that the dependent variable has not been transformed...