Nonconvex penalties such as the smoothly clipped absolute deviation or minimax concave penalties have desirable properties such as the oracle property, even when the dimension of the predictive variables is large. However, checking whether a given local minimizer has such properties is not easy...

We propose an approximated penalized estimator (APE) that covers various statistical models and nonconvex penalties including the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) as a special case. The APE achieves the oracle property with a diverging number of parameters...

In this paper, we propose a method of quadratic approximation that unifies various types of smoothly clipped absolute deviation (SCAD) penalized estimations. For convenience, we call it the quadratically approximated SCAD penalized estimation (Q-SCAD). We prove that the proposed Q-SCAD estimator...

In cancer classification based on gene expression data, it would be desirable to defer a decision for observations that are difficult to classify. For instance, an observation for which the conditional probability of being cancer is around 1/2 would preferably require more advanced tests rather...

Logistic random-effects models are often employed in the analysis of correlated binary data. However, fitting these models is challenging, since the marginal distribution of the response variables is analytically intractable. Often, the random effects are treated as missing data for constructing...