-We study the least square regression with data dependent hypothesis and coefficient regularization algorithms based on general kernel. An explicit expression of the solution of this kernel scheme is derived. Then we provide a sample error with a decay of 1 ( ) O m and estimate the approximation error in terms of some kind of K -functional. Index Terms -Least Square Regressions, Data Dependent ...

It is very common to examine reliability of triage scales using (weighted) kappa statistics. The point is that weighted kappa has grossly underestimated disagreements by one category and put more emphasis on extreme category disagreements; therefore, low prevalence of critically-ill and non-urgent patients has excluded the effect of extreme categories disagreement from calculated kappa coeffici...

We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives. This is a preliminary result to the study...

Diffusion-weighted magnetic resonance imaging data obtained early in the course of therapy can be used to estimate tumor proliferation rates, and the estimated rates can be used to predict tumor cellularity at the conclusion of therapy. Six patients underwent diffusion-weighted magnetic resonance imaging immediately before, after one cycle, and after all cycles of neoadjuvant chemotherapy. Appa...

We consider nonparametric estimation of coefficient functions in a varying coefficient model of the form Yij = X T i (tij)β(tij)+ i(tij) based on longitudinal observations {(Yij ,Xi(tij), tij), i = 1, . . . , n, j = 1, . . . , ni}, where tij and ni are the time of the jth measurement and the number of repeated measurements for the ith subject, and Yij and Xi(tij) = (Xi0(tij), . . . ,XiL(tij)) T...

We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero within certain sub-regions. Besides identifying the null region in which the coefficient function is zero, we also aim to perform estimation and inferences for the nonparametrically estimated coefficient function without over-shrinking the...