Abstract
We consider methods for parameter estimation of the shifted power transformation. The ordinary likelihood function is unbounded and then fails to have a local maximum. This is a non-regular problem in likelihood because the range of observations depends on the unknown shift parameter. To avoid such a difficulty, we discuss the group likelihood method and the maximum product of spacings method, in a univariate case, assuming the power-normal distribution as an underlying distribution for observations. We describe the computational procedures for parameter estimation. To evaluate the performance of the estimates from the two methods, we perform a simulation study. In addition, two examples are given to illustrate some aspects of the two methods.
