Likelihood Inference under a Transformed Truncated-Normal Nonlinear Model with Heteroscedastic Errors

Abstract

Box and Cox (1964) proposed a transformed normal linear model with homoscedastic errors for modeling independent continuous data utilizing any family of parametric monotone transformations. However, when the range of a monotone transformation is different from the set of all real numbers, data after this monotone transformation cannot be normally distributed. For example, any transformation in the family of power transformations has range different from the set of all real numbers except for the log transformation. In this talk, we extend their model by proposing a transformed truncated-normal nonlinear model with heteroscedastic errors for modeling continuous data utilizing any family of parametric monotone transformations. Some theoretical results of the proposed model will be discussed including maximum likelihood estimation, hypothesis testing, confidence regions, and quantile estimation of a future observation.