A Comparison of Methods for Parameter Estimation of the Shifted Power Transformation

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.