  Sure screening technique has been considered as a powerful tool to handle the
ultrahigh dimensional variable selection problems, where the dimensionality p
and the sample size n can satisfy the NP dimensionality log p=O(n^a) for some
a>0 (Fan & Lv 2008). The current paper aims to simultaneously tackle the
"universality" and "effectiveness" of sure screening procedures. For the
"universality", we develop a general and unified framework for nonparametric
screening methods from a loss function perspective. Consider a loss function to
measure the divergence of the response variable and the underlying
nonparametric function of covariates. We newly propose a class of loss
functions called conditional strictly convex loss, which contains, but is not
limited to, negative log likelihood loss from one-parameter exponential
families, exponential loss for binary classification and quantile regression
loss. The sure screening property and model selection size control will be
established within this class of loss functions. For the ``effectiveness", we
focus on a goodness of fit nonparametric screening (Goffins) method under
conditional strictly convex loss. Interestingly, we can achieve a better
convergence probability of containing the true model compared with related
literature. The superior performance of our proposed method has been further
demonstrated by extensive simulation studies and some real scientific data
example.
