  In this paper, a kernel least mean absolute third (KLMAT) algorithm is
developed for adaptive prediction. Combining the benefits of the kernel method
and the least mean absolute third (LMAT) algorithm, the proposed KLMAT
algorithm performs robustly against noise with different probability densities.
To further enhance the convergence rate of the KLMAT algorithm, a variable
step-size version (VSS-KLMAT algorithm) is proposed based on a Lorentzian
function. Moreover, the stability and convergence property of the proposed
algorithms are analyzed. Simulation results in the context of time series
prediction demonstrate that the effectiveness of proposed algorithms.
