MASS RECENTRED KERNEL SMOOTHERS

The local linear smoother usually gives better performance than the Na daraya-Watson smoother. An exception is the case of data sparsity. Her e we discuss a modification of the Nadaraya-Watson smoother by Muller & Song (1993), based on a horizontal shift of the kernel weights towar ds the local centre of mass of the design points. This gives performan ce similar to the local linear when that works well and better perform ance when it does not. The new smoother also preserves monotonicity. S hifting towards the centre of mass is also used to develop a modified kernel density estimate which cancels the well-known peak spreading ef fect.