Leapfrog estimation of a fixed-effects model with unknown transformation of the dependent variable

This paper considers a fixed-effects panel version of the linear transformation model, in which the dependent variable is h(yt) for an unspecified, strictly monotonic h. Examples of the model include the multiple-spell proportional hazards model and dependent-variable transformation models (e.g., the Box–Cox model) with fixed effects. A semiparametric estimator, called the leapfrog estimator, is introduced and shown to be n-consistent and asymptotically normal. The leapfrog estimator allows for h to vary over time and for heteroskedasticity across observational units. Related semiparametric estimators are considered, and a general covariance result for estimators based on second-order U-processes is presented.