Authors: Sai K. Popuri and Nagaraj K. Neerchal
Abstract: Random variables that feature a point mass at zero and are continuous on the positive real line are said to follow a semi-continuous distribution. The density functions of such random variables have a discrete and a continuous component. When the probability of realizing zero is not a function of the parameter that governs the continuous component, the density function is called a two-part model. In this short paper, we present a simple graphical procedure based on the parametric bootstrap method to test whether a given functional dependence exist between the probability of realizing zero and the parameter from the continuous component in a given two-part model. Results from a simulation study suggest that the proposed procedure could be viewed as a simple empirical alternative to the score test.
Keywords: Semi-continuous; Two-part; Score test; Tobit; Parametric restriction