  Sufficient dimension reduction aims for reduction of dimensionality of a
regression without loss of information by replacing the original predictor with
its lower-dimensional subspace. Partial (sufficient) dimension reduction arises
when the predictors naturally fall into two sets, X and W, and we seek
dimension reduction on X alone while considering all predictors in the
regression analysis. Though partial dimension reduction is a very general
problem, only very few research results are available when W is continuous. To
the best of our knowledge, these methods generally perform poorly when X and W
are related, furthermore, none can deal with the situation where the reduced
lower-dimensional subspace of X varies dynamically with W. In this paper, We
develop a novel dynamic partial dimension reduction method, which could handle
the dynamic dimension reduction issue and also allows the dependency of X on W.
The asymptotic consistency of our method is investigated. Extensive numerical
studies and real data analysis show that our {\it Dynamic Partial Dimension
Reduction} method has superior performance comparing to the existing methods.
