SiZer for smoothing splines (Q2488419)

SiZerSS is a shortening for ``Significant Zero crossing of derivatives for smoothing splines''. This is a 2D graphical display at which for a smoothing spline \(\hat f_\lambda(x)\) (\(\lambda\in[\lambda_{\min},\lambda_{\max}]\) being a smoothing parameter) a point with coordinates \((\lambda,x)\) is marked by its colour if \((\partial/\partial x)\widehat f_\lambda(x)\) is significantly positive, negative, \(\simeq 0\), or if the data are too sparse at \(x\) to make significant statements. Construction of SiZerSS is described and the choice of \(\lambda_{\min},\lambda_{\max}\) is discussed. The case of binned data is also considered. Results of simulations and application to family food expenditures in UK are considered.