NONPARAMETRIC TRANSFORMATIONS FOR BOTH SIDES OF A REGRESSION-MODEL

One way to model heteroscedasticity and skewness of the error distribu tion in regression is to transform both sides of the regression equati on. If it is possible to transform the regression equation to result i n normally distributed errors, then we can obtain more efficient param eter estimates and valid prediction intervals. One problem with this a pproach is that the choice of transformation is usually restricted to the power or shifted power family. Often there is no scientific basis for this model and the limited flexibility of this parametric family m ay miss important features of the distribution. A more comprehensive a pproach is to estimate the transformation by using nonparametric metho ds based on maximizing a penalized likelihood function. This maximizat ion problem leads naturally to a spline estimate for the log-derivativ e of the transformation. An algorithm for computing the estimate is gi ven along with results on the existence and uniqueness of the estimate . This nonparametric method is illustrated by using a non-normally dis tributed fisheries data set.