Targeted principal components regression

We propose a principal components regression method based on maximizing joint pseudo-likelihood for responses and predictors. Our uses both predictors to select linear combinations of the relevant regression, thereby addressing an oft-cited deficiency conventional regression. The proposed estimator is shown be consistent in wide range settings, including ones with non-normal dependent observations; conditions first second moments suffice if number (p) fixed, observations (n) tends infinity, dependence weak, while stronger distributional assumptions are needed when p→∞ n. obtain estimator’s asymptotic distribution as projection multivariate normal random vector onto tangent cone parameter set at true parameter, find asymptotically more efficient than competing ones. In simulations our substantially accurate compares favorably partial least squares predictor envelopes. method’s practical usefulness illustrated data example cross-sectional prediction stock returns.