A New Kind Of Singular Value Penalty Of Reduced Rank Regression

With the Advance of technology,we always meet various of big data in appli-cation,such as securities market transaction data,multimedia graphics and video da-ta,aerospace collection data,biometric data,and so on.These data are usually called high dimensional data in statistical processing.In this article,we propose a thresholded singular value penalization approach for low-rank matrix approximation,and use it to discover a new reduced rank estimation method for high-dimensional multivariate re-gression.In other words,this article discovers the high-dimensional type of the model(Zheng,2014).The thresholded singular value penalization is defined as the thresh-olding penalty of the singular values of the matrix.It is almost always non-convex decreasing with the singular value of the matrix.However,an algorithm based on the local linear approximation(LLA)for minimizing the penalized function for a broad class of the non-convex penalty functions proposed by Zou and Li can naturally adopt a low-rank representation.The one-step LLA estimation method will reduce the com-putational cost in minimizing the non-convex penalized function at the most low-rank situation.We can use it to study the thresholded singular value penalization problem easily.At the end of this article,we also use our new model to study in genetics demon-strate and compare with other methods,and give proof of our theorems in the appendix.