Local polynomial regression with an ordinal covariate

We are interested in fitting a nonparametric regression model to data when the covariate is an ordered categorical variable. We extend the local polynomial estimator, which normally requires continuous covariates, to a local polynomial estimator that allows for ordered categorical covariates. We derive the asymptotic conditional bias and variance under the assumption that the categories correspond to quantiles of an unobserved continuous latent variable. We conduct a simulation study with two patterns of ordinal data to evaluate our estimator.