Comparison of Methods for Monotone Nonparametric Multiple Regression

The weighted chi-squared test for dimension is an extension to the chi-squared test associated with sliced inverse regression as it lifts restrictive distributional assumptions on the predictors. Its usage requires the estimation of the mixture weights which may affect accuracy, and the computationally intensive calculation of percentiles of a mixture chi-squared distribution. The scaled and adjusted chi-squared corrections to the mixture chi-squared distribution have been proposed as alternatives to the weighted chisquared test. A simulation study assessing power performance of the four tests indicates that the computationally simple adjusted chi-squared test could be used in place of the weighted chi-squared test, whereas the scaled chi-squared test performs much worse.