Conditional feature screening for mean and variance functions in models with multiple-index structure (Q1639572)

The conditional feature screening procedures were proposed for the mean and variance functions respectively in the following heteroscedastic regression model \[ Y=g_\mu (X^T\beta^1,\dots, X^T\beta^K ) + g_\nu ( X^T\theta^1,\dots, X^T\theta^L)\varepsilon, \] where \(g_\mu\) and \(g_\nu\) are unknown smooth functions, \(X\) is a vector of \(p\) predictors, \(\beta^k\) and \(\theta^l\) correspondingly denote coefficients of the \(k\)th index in mean function and \(l\)th index in variance function, \(\varepsilon\) is independent of \(X\) with zero mean and unit variance. The sure screening properties of the feature screening approaches were studied. The proposed procedures have sure screening properties in the sense that they do not need to estimate the nonparametric link functions in semiparametric models. The results of simulation studies and a real data analysis are included to demonstrate the high performance in the case of high correlation among the variables. The proposed conditional feature screening procedures are expected to be particularly efficient for ultrahigh-dimensional models.