Permuted Inclusion Criterion: A Variable Selection Technique

We introduce a new variable selection technique called the Permuted Inclusion Criterion (PIC) based on augmenting the predictor space X with a row-permuted version denoted Xpi. We adopt the linear regression setup with n observations on p variables. Thus, our augmented space has p real predictors and p permuted predictors. This has many desirable properties for variable selection. For example, this preserves relations between variables, e.g. squares and interactions and equates the moments and covariance structure of X and Xpi. More importantly, Xpi scales with the size of X. We motivate the idea with forward selection. The first time we select a predictor from Xpi, we stop. As this depends on the permutation, we simulate many times and create a distribution of models and stopping points. This has the added benefit of quantifying how certain we are about stopping. Variable selection typically penalizes each additional variable by a prespecified amount. Our method uses a data-adaptive penalty. We apply this method to simulated data and compare its predictive performance to other widely used criteria such as Cp, RIC, and the Lasso. Viewing PIC as a selection scheme for greedy algorithms, we extend the PIC to generalized linear regression (GLM) and classification and regression trees (CART)

Variable-mesh difference equation for the stream function in axially symmetric flow

"December 6, 1964.""Reprinted from AIAA Journal 1964."A finite difference equation is developed for the stream function in cylindrical coordinates with axial symmetry which is applicable to an irregular mesh having different length and radial dimensions. In addition, the length and radial dimensions may be varied, and the mesh made finer in any interior region. The equation also takes into account an irregular boundary