Bruce E. Hansen
Sample Splitting and Threshold Estimation
University of Wisconsin–Madison
threshold models wide variety applications economics direct applications include models separating multiple equilibria applications include empirical sample splitting sample split based continuouslydistributed variable firm size addition threshold models may used parsimonious strategy nonparametric function estimation example threshold autoregressive model tar popular nonlinear time series literature threshold models also emerge special cases complex statistical frameworks mixture models switching models markov switching models smooth transition threshold models may important understand statistical properties threshold models preliminary step development statistical tools handle complicated structures despite large number potential applications statistical theory threshold estimation undeveloped known threshold estimates superconsistent distribution theory useful testing inference yet provided paper develops statistical theory threshold estimation regression context allow either crosssection time series observations least squares estimation regression parameters considered asymptotic distribution theory regression estimates threshold regression slopes developed found distribution threshold estimate nonstandard method construct asymptotic confidence intervals developed inverting likelihood ratio statistic shown yields asymptotically conservative confidence regions monte carlo simulations presented assess accuracy asymptotic approximations empirical relevance theory illustrated application multiple equilibria growth model durlauf johnson 1995