Practical Smoothing: The Joys of P-splinesCambridge University Press, 18 mrt 2021 - 208 pagina's This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers. |
Inhoudsopgave
Bases Penalties and Likelihoods | 6 |
Optimal Smoothing in Action | 36 |
Multidimensional Smoothing | 59 |
Smoothing of Scale and Shape | 84 |
Complex Counts and Composite Links | 103 |
Special Subjects | 131 |
Appendix A Psplines for the Impatient | 159 |
Array Algorithms | 174 |
| 188 | |
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Practical Smoothing: The Joys of P-splines Paul H.C. Eilers,Brian D. Marx Gedeeltelijke weergave - 2021 |
Veelvoorkomende woorden en zinsdelen
20 segments additive model algorithm Appendix B-spline basis matrix B-spline coefficients basis functions Bayesian binomial coefficient vector columns components compute counts covariance cross-validation cubic B-spline data set density estimation difference penalty domain Dutch boys effective dimension Eilers and Marx equations error bands example expectile curves fitted curve gamlss grid harmonic penalty HFS algorithm histogram identity matrix iterative knots Laplace approximation least squares linear predictor link function logarithm mixed model number of B-splines number of observations objective function Old Faithful optimal P-spline fit package PCLM penalized Poisson Poisson distribution polynomial quadratic quantile quantile curves random effects regressors residuals roughness penalty rows second-order differences second-order penalty Section shows signal regression sparse sparse matrix splines standard deviation standard error sum of squares tensor product basis tensor product P-splines third-order penalty truncated truncated power functions two-dimensional values variable variance weights Whittaker smoother zero