Delgado, M.A. and J. Mora
Investigaciones Económicas – 19.3 (1995), 435-467

Keywords: nonparametric regression, semiparametric inference, discrete regressors, kernel estimation, k-NN estimation

Abstract: This paper deals with the practical situation of estimating nonparametric and semiparametric models when some or all regressors are discrete. When all regressors are discrete, Delgado and Mora (1995) show that a naive non-smoothing estimate produces globally consistent estimates of the regression function. Here we discuss that, in certain circumstances, it is advisable to use a smooth estimate. We show that the most popular smoothers, like kernels or k-NN, are asymptotically equivalent to the non-smoothing estimate. We also consider the mixed case where some regressors are discrete and others are continuous. The nonparametric estimates we present are useful in semiparametric problems. We discuss in detail the partially linear regression model and shape-invariant modelling. The paper also includes a Monte Carlo study.