2012/01/03 by Luo Xiao, Xiao, Luo, Yingxing Li +5
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1201.0708
34 pages, 1 figure
arxiv created 2012/06/10 · arxiv updated 2012/06/12
This report studies local asymptotics of P-splines with pth degree B-splines and a mth order difference penalty. Earlier work with p and m restricted is extended to the general case. Asymptotically, penalized splines are kernel estimators with equivalent kernels depending on m, but not on p. A central limit theorem provides simple expressions for the asymptotic mean and variance. Provided it is fast enough, the divergence rate of the number of knots does not affect the asymptotic distribution. The optimal convergence rate of the penalty parameter is given.