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Abstract:
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Threshold regression models are useful for identifying subgroups with heterogenous parameters. The conventional threshold regression models split the sample based on a single and observed threshold variable, which enforces the threshold point to be the same for all subgroups of population. To relax this rigid assumption, we consider a more flexible single-index threshold model in the quantile regression setup, where the sample is split based on a single index, an unknown linear combination of predictors. To account for the complication in the asymptotic theory caused by the nonregularity of the model, we propose a smoothed estimator for the regression coefficients and index parameters, and establish its asymptotic properties at a single quantile as well as for the quantile process. Furthermore, we propose a Wald-type test and a mixed-bootstrap procedure for inference on the index parameters.
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