Abstract:

Based on nonparametric Bayesian estimation of a conditional distribution, posterior estimation of an unknown regression function is obtained by calculating its expectation. The mean square error of the estimation is calculated. Its convergence in mean square of the estimation is proved. It is shown that the mean square error of the estimation is less than that of the local linear kernel regression when prior regression is chosen to be close to the unknown regression function. Empirical evidence shows that the nonparametric Bayesian regression may be more effective in prediction than local linear regression.

Key words: nonparametric Bayesian regression, nonparametric Bayesian distribution estimation, Dirichlet process, local linear regression, population prediction