Influence diagnostics for the power-normal Tobit model

Abstract

Diagnostic analysis tools are studied for the censored power-normal Tobit regression model. We follow the Cook’s (J. R. Stat. Soc., Ser. B, Stat. Methodol. 48 (1986) 133–169) approach, and several perturbation schemes are considered to detect influential observations. In particular, closed-form expressions of the normal curvatures for studying local influence are obtained under some perturbation schemes. The approach pursued also considers separate analysis for regression and scale-asymmetry parameters. Further, we define residuals to identify departures from the model assumptions, as well as to assess the overall goodness-of-fit of the censored power-normal Tobit regression model. The diagnostic measures developed are applied in a real data set for illustrative purposes.