Bayesian variants of some classical semiparametric regression techniques

Abstract

This paper develops new Bayesian methods for semiparametric inference in the partial linear Normal regression model: y=zβ+f(x)+var epsilon where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity. Methods for testing parametric regression models against semiparametric alternatives are developed. We discuss how these methods can, at some cost in terms of computational complexity, be extended to other models (e.g. qualitative choice models or those involving censoring or truncation) and provide precise details for a semiparametric probit model. We show how the assumption of Normal errors can easily be relaxed

The wages of BMI: Bayesian analysis of a skewed treatment–response model with nonparametric endogeneity

“…Though several approaches could be employed to handle this issue, our approach to a nonparametric treatment of f s follows that described in Koop and Poirier (2004).…”

“…As described in Koop and Poirier (2004), an informative prior on g can be used to surmount the problem of insufficient observations when k D n, and also to introduce the possibility of smoothing the regression curve. To this end, we reparameterize the model in terms of the quantity y Á Hg, where…”

“…0, the first differences of pointwise slopes are imposed to be equal, resulting in f being linear (with 1 and 2 defining the intercept and slope of the line). Moderate values of Á will result in smoothed regression curves, while choosing Á to be too large will produce regression functions that are excessively erratic (see Koop and Poirier (2004) for more details). Putting (9) and (10) together, we obtain a prior for y of the form…”

Bayesian Treatments for Panel Data Stochastic Frontier Models with Time Varying Heterogeneity

“…Instead of resorting to the classical nonparametric regression techniques (Kneip et al 2012), a Markov chain Monte Carlo (MCMC) algorithm is implemented to estimate the model. We can consider this to be a generalization of Koop and Poirier (2004) in the case of panel data, including both individual-specific and time-varying effects. Moreover, our model does not rely on the restrictive conjugate prior formulation for the time varying individual-effects.…”

“…The posterior is well-defined and integrable. Such issues have been dealt with by Koop and Poirier (2004), whose spline method is equivalent to the difference prior we adopt. To proceed with further inference, we need to solve this analytically.…”