|
Abstract:
|
The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. It is shown that the ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has posterior mean given by weighted least-squares (WLS), and posterior covariance matrix given by the heteroscedastic-consistent sandwich estimator, according to a pairs-bootstrap distribution approximation. Also, for a particular choice of MDP baseline prior, this WLS solution provides a new type of generalized ridge regression estimator, which can handle multicollinear or singular design matrices even when the number of covariates exceeds the sample size, and which shrinks the coefficient estimates of irrelevant covariates towards zero. Hence the approach is useful for flexible nonlinear regression. This MDP/OLS functional methodology can be extended to methods of analyzing the sensitivity of estimates of a causal effect, over a range of hidden biases due to missing covariates that are omitted from the regression. The methodology is illustrated with the analysis of simulated and real data. This includes Vibrations of Effects (VoE) analyses.
|
