Abstract
Non-negative ordered survey data often exhibit an unusually high frequency of zeros in the first interval. Zero-inflated interval regression models handle the excess of zeros by combining a split probit model and an ordered probit model. In the presence of data violating distributional assumptions, standard inference based on the maximum likelihood method gives biased estimates with large standard errors. In this paper, we consider robust inference based on the exponential tilting methodology for the zero-inflated interval regression model. The application considers data on cyber security to study the relationship between investments in cyber defences and losses from cyber breaches. Robust estimates obtained via tilting clearly show an effect of the investments in reducing the loss amount.