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References

Published online by Cambridge University Press:  25 February 2021

Paul H.C. Eilers  and
Brian D. Marx
Paul H.C. Eilers
Affiliation:
Erasmus Universiteit Rotterdam
Brian D. Marx
Affiliation:
Louisiana State University
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Practical Smoothing
The Joys of P-splines
 , pp. 188 - 195
Publisher: Cambridge University Press
Print publication year: 2021

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References

Aguilera, A. M., Aguilera-Morillo, M. C., and Preda, C. 2016. Penalized versions of functional PLS regression. Chemometrics and Intelligent Laboratory Systems, 154(May 15), 80–92.Google Scholar
Aguilera-Morillo, M. C., and Aguilera, A. M. 2015. P-spline estimation of functional classification methods for improving the quality in the food industry. Communications in Statistics – Simulation and Computation, 44(10, SI), 2513–2534.CrossRefGoogle Scholar
Aitkin, M., Francis, B., and Hinde, J. 2005. Statistical Modelling in GLIM 4. 2nd ed. Oxford Statistical Science Series, Oxford, UK.Google Scholar
Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.Google Scholar
Ayma, D., Durbán, M., Lee, D.-J., and Eilers, P. H. C. 2016. Penalized composite link models for aggregated spatial count data: A mixed model approach. Spatial Statistics, 17, 179–198.Google Scholar
Azzalini, A., and Bowman, A. W. 1990. A look at some data on the Old Faithful geyser. Journal of the Royal Statistical Society, Series C, 39, 357–365.Google Scholar
Basford, K. E., Mclachlan, G. J., and York, M. G. 1977. Modelling the distribution of stamp paper thickness via finite normal mixtures: The 1872 Hidalgo stamp issue of Mexico revisited. Journal of Applied Statistics, 24, 169–180.Google Scholar
Bollaerts, K., Eilers, P. H. C., and Aerts, M. 2006. Quantile regression with monotonicity restrictions using P-splines and the L1-norm. Statistical Modelling, 6, 189–207.Google Scholar
Braun, J., Duchesne, T., and Stafford, J. E. 2005. Local likelihood density estimation for interval censored data. The Canadian Journal of Statistics, 33, 39–60.Google Scholar
Bro, R. 1999. Exploratory study of sugar production using fluorescence spectroscopy and multi-way analysis. Chemometrics and Intelligent Laboratory Systems, 46, 133–147.CrossRefGoogle Scholar
Camarda, C. G. 2012. Mortalitysmooth: An R package for smoothing Poisson counts with P-splines. Journal of Statistical Software, 50, 1–24.Google Scholar
Camarda, C. G., Eilers, P. H. C., and Gampe, J. 2008. Modelling general patterns of digit preference. Statistical Modelling, 8, 385–401.Google Scholar
Camarda, C. G., Eilers, P. H. C., and Gampe, J. 2016. Sums of smooth exponentials to decompose complex series of counts. Statistical Modelling, 16(4), 279–296.Google Scholar
Camarda, C. G., Eilers, P. H. C., and Gampe, J. 2017. Modelling trends in digit preference patterns. Journal of the Royal Statistical Society, Series C, 66(5), 893–918.Google Scholar
Claeskens, G., Krivobokova, T., and Opsomer, J. D. 2009. Asymptotic properties of penalized spline estimators. Biometrika, 96, 529–544.Google Scholar
Currie, I. D. 2019. Forecasting with penalty functions – Part III. www.longevitas.co.uk/site/informationmatrix/forecastingwithpenalty functionspart3.html.Google Scholar
Currie, I. D., and Durbán, M. 2002. Flexible smoothing with P-splines: A unified approach. Statistical Modelling, 2, 333–349.Google Scholar
Currie, I. D., Durbán, M., and Eilers, P. H. C. 2004. Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.CrossRefGoogle Scholar
Currie, I. D., Durbán, M., and Eilers, P. H. C. 2006. Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society, Series B, 68, 259–280.Google Scholar
de Boor, C. 2001. A Practical Guide to Splines, rev. ed. New York: Springer-Verlag.Google Scholar
De Gruttola, V., and Lakatos, S. W. 1989. Analysis of doubly censored survival data, with applications to AIDS. Biometrics, 45, 1–11.Google Scholar
de Rooi, J. J., Devos, O., Sliwa, M., Ruckebusch, C., and Eilers, P. H. C. 2013. Mixture models for two-dimensional baseline correction, applied to artifact elimination in time-resolved spectroscopy. Analytica Chimica Acta, 771(Apr 10), 7–13.Google Scholar
de Rooi, J. J., and Eilers, P. H. C. 2012. Mixture models for baseline estimation. Chemometrics and Intelligent Laboratory Systems, 117(SI), 56–60.Google Scholar
de Rooi, J. J., van der Pers, N. M., Hendrikx, R. W. A., Delhez, R., Böttger, A. J., and Eilers, P. H. C. 2014. Smoothing of X-ray diffraction data and Kα2 elimination using penalized likelihood and the composite link model. Journal of Applied Crystallography, 47, 852–860.Google Scholar
Dierckx, P. 1993. Curve and Surface Fitting with Splines. Oxford: Clarendon Press.Google Scholar
Dobson, A. J., and Barnett, A. G. 2018. An Introduction to Generalized Linear Models, 4th ed. Boca Raton, FL: CRC Press.Google Scholar
Efron, B. 1988. Logistic regression, survival analysis, and the Kaplan–Meier curve. Journal of the American Statistical Association, 83, 414–425.Google Scholar
Eilers, P. H. C. 1998. Hazard smoothing with B-splines. In: Marx, B. D., and Friedl, H. (eds.), Proceedings of the 13th International Workshop on Statistical Modeling, pp. 200–207. Baton Rouge: Louisiana State University.Google Scholar
Eilers, P. H. C. 1999. Discussion on: The analysis of designed experiments and longitudinal data by using smoothing splines. Journal of the Royal Statistical Society, Series C, 48, 307–308.Google Scholar
Eilers, P. H. C. 2003. A perfect smoother. Analytical Chemistry, 75, 3631–3636.Google Scholar
Eilers, P. H. C. 2005. Unimodal smoothing. Journal of Chemometrics, 19, 317–328.Google Scholar
Eilers, P. H. C. 2007. III-posed problems with counts, the composite link model and penalized likelihood. Statistical Modelling, 7, 239–254.Google Scholar
Eilers, P. H. C. 2012. Composite link, the neglected model. In: Komarek, A., and Nagy, S. (eds.), Proceedings of the 27th International Workshop on Statistical Modelling, pp. 11–22. Prague: Tribun EU.Google Scholar
Eilers, P. H. C. 2017. Uncommon penalties for common problems. Journal of Chemometrics, 31(4, SI), 2878.Google Scholar
Eilers, P. H. C., and Borgdorff, M. W. 2007. Non-parametric log-concave mixtures. Computational Statistics & Data Analysis, 51, 5444–5451.Google Scholar
Eilers, P. H. C., Currie, I. D., and Durbán, M. 2006. Fast and compact smoothing on large multidimensional grids. Computational Statistics & Data Analysis, 50, 61–76.Google Scholar
Eilers, P. H. C., and de Menezes, R. X. 2005. Quantile smoothing of array CGH data. Bioinformatics, 21, 1146–1153.Google Scholar
Eilers, P. H. C., Gampe, J., Marx, B. D., and Rau, R. 2008. Modulation models for seasonal time series and incidence tables. Statistics in Medicine, 27, 3430–3441.Google Scholar
Eilers, P. H. C., and Goeman, J. J. 2004. Enhancing scatterplots with smoothed densities. Bioinformatics, 20, 623–628.Google Scholar
Eilers, P. H. C., Li, B., and Marx, B. D. 2009. Multivariate calibration with single-index signal regression. Chemometrics and Intelligent Laboratory Systems, 96, 196–202.Google Scholar
Eilers, P. H. C., and Marx, B. D. 1992. Generalized linear models with P-splines. In: Fahrmeir, L. et al. (eds.), Advances in GLIM and Statistical Modelling. New York: Springer.Google Scholar
Eilers, P. H. C., and Marx, B. D. 1996. Flexible smoothing using B-splines and penalties (with comments and rejoinder). Statistical Science, 11, 89–121.CrossRefGoogle Scholar
Eilers, P. H. C., and Marx, B. D. 2002. Generalized linear additive smooth structures. Journal of Computational and Graphical Statistics, 11, 758–783.Google Scholar
Eilers, P. H. C., and Marx, B. D. 2003. Multivariate calibration with temperature interaction using two-dimensional penalized signal regression. Chemometrics and Intelligent Laboratory Systems, 66, 159–174.Google Scholar
Eilers, P. H. C., and Marx, B. D. 2010. Splines, knots and penalties. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 637–653.Google Scholar
Eilers, P. H. C., Marx, B. D., and Durbán, M. 2015. Twenty years of P-splines. SORT-Statistics and Operations Research Transactions, 39(2), 149–186.Google Scholar
Fahrmeir, L., Kneib, T., and Lang, S. 2004. Penalized structured additive regression for space-time data: A Bayesian perspective. Statistica Sinica, 14, 731–761.Google Scholar
Fahrmeir, L., and Tutz, G. 2001. Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd ed. New York: Springer.CrossRefGoogle Scholar
Fan, J., and Gijbels, I. 1996. Local Polynomial Modelling and Its Applications. London: Chapman and Hall.Google Scholar
Fellner, W. H. 1986. Robust estimation of variance components. Technometrics, 28(1), 51–60.Google Scholar
Frank, I. E., and Friedman, J. H. 1993. A statistical view of some chemometric regression tools. Technometrics, 35, 109–148.Google Scholar
Frasso, G., and Eilers, P. H. C. 2015. L- and V-curves for optimal smoothing. Statistical Modelling, 15, 91–111.Google Scholar
Gentle, J. E. 2009. Computational Statistics. New York: Springer.Google Scholar
Gressani, O., and Lambert, P. 2018. Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines. Computational Statistics and Data Analysis, 124, 151–167.Google Scholar
Greven, S., and Scheipl, F. 2017. A general framework for functional regression modelling. Statistical Modelling, 17, 1–35.Google Scholar
Hall, P., and Opsomer, J. D. 2005. Theory for penalised spline regression. Biometrika, 92(1), 105–118.Google Scholar
Hansen, P. C. 1992. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34(4), 561–580.Google Scholar
Härdle, W. 1992. Applied Nonparametric Regression. Cambridge: Cambridge University Press.Google Scholar
Harville, D. A. 1977. Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72, 320–338.Google Scholar
Hasselblad, V., Stead, A. G., and Galke, W. 1980. Analysis of coarsely grouped data from the lognormal distribution. Journal of the American Statistical Association, 75, 771–778.Google Scholar
Hastie, T. J., Buja, A., and Tibshirani, R. J. 1995. Penalized discriminant analysis. The Annals of Statistics, 23, 73–102.Google Scholar
Hastie, T. J., and Tibshirani, R. J. 1990. Generalized Additive Models. London: Chapman and Hall.Google Scholar
Hastie, T. J., and Tibshirani, R. J. 1993. Varying-coefficient models. Journal of the Royal Statistical Society, Series B, 55, 757–796.Google Scholar
Hastie, T. J., Tibshirani, R. J., and Friedman, J. H. 2009. Elements of Statistical Learning: Data Mining, Inference and Prediction. 2nd ed. New York: Springer.Google Scholar
Henderson, C. R. 1975. Best linear unbiased estimation and prediction under a selection model. Biometrics, 31, 423–447.Google Scholar
Hutchinson, M. F., and de Hoog, F. R. 1986. Smoothing noisy data with spline functions. Numerische Mathematik, 50(3), 311–319.Google Scholar
Hyndman, R. 2014. Fast computation of cross-validation in linear models. https://robjhyndman.com/hyndsight/loocv-linear-models/.Google Scholar
Jarrow, R., Ruppert, D., and Yu, Y. 2004. Estimating the interest rate term structure of corporate debt with a semiparametric penalized spline model. Journal of the American Statistical Association, 99, 57–66.CrossRefGoogle Scholar
Jullion, A., and Lambert, P. 2007. Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models. Computational Statistics & Data Analysis, 51, 2542–2558.Google Scholar
Kauermann, G., Krivobokova, T., and Fahrmeir, L. 2009. Some asymptotic results on generalized penalized spline smoothing. Journal of the Royal Statistical Society, Series B, 71, 487–503.Google Scholar
Kauermann, G., Krivobokova, T., and Semmler, W. 2011. Filtering time series with penalized splines. Studies in Nonlinear Dynamic & Econometrics, 15, 1–26.Google Scholar
Keiding, N. 1991. Age-specific incidence and prevalence – a statistical perspective. Journal of the Royal Statistical Society, Series A, 154, 371–412.Google Scholar
Kneib, T. 2013. Beyond mean regression. Statistical Modelling, 13, 275–303.Google Scholar
Koenker, R. 2005. Quantile Regression. Cambridge: Cambridge University Press.Google Scholar
Koenker, R., and Bassett, G. 1978. Regression quantiles. Econometrica, 46, 33–50.Google Scholar
Kooperberg, C., and Stone, C. J. 1991. A study of logspline density estimation. Computational Statistics and Data Analysis, 12, 327–348.Google Scholar
Lambert, P. 2011. Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data. Computational Statistics & Data Analysis, 55, 429–445.Google Scholar
Lambert, P., and Eilers, P. H. C. 2005. Bayesian proportional hazards model with time-varying regression coefficients: A penalized Poisson regression approach. Statistics in Medicine, 24, 3977–3989.Google Scholar
Lambert, P., and Eilers, P. H. C. 2009. Bayesian density estimation from grouped continuous data. Computational Statistics & Data Analysis, 53, 1388–1399.Google Scholar
Lang, S., Adebayo, S. B., Fahrmeir, L., and Steiner, W. J. 2003. Bayesian geoadditive seemingly unrelated regression. Computational Statistics, 18, 263–292.Google Scholar
Lee, D.-J., and Durbán, M. 2009. Smooth-CAR mixed models for spatial count data. Computational Statistics & Data Analysis, 53, 2968–2979.Google Scholar
Lee, D.-J., Durbán, M., and Eilers, P. H. C. 2013. Efficient two-dimensional smoothing with P-spline ANOVA mixed models and nested bases. Computational Statistics & Data Analysis, 61, 22–37.Google Scholar
Lee, Y., Nelder, J. A., and Pawitan, Y. 2006. Generalized Linear Models with Random Effects. Boca Raton, FL: CRC Press.Google Scholar
Lee, Y., Nelder, J. A., and Pawitan, Y. 2017. Generalized Linear Models with Random Effects, 2nd ed. Boca Raton, FL: CRC Press.Google Scholar
Li, B., and Marx, B. D. 2008. Sharpening P-spline signal regression. Statistical Modelling, 8, 367–383.Google Scholar
Li, Y., and Ruppert, D. 2008. On the asymptotics of penalized splines. Biometrika, 95, 415–436.Google Scholar
Liao, X., and Meyer, M. C. 2019. cgam: An R package for the constrained generalized additive model. Journal of Statistical Software, 89, Issue 5, 1–24.Google Scholar
Loader, C. 1999. Local Regression and Likelihood. New York: Springer.Google Scholar
Marx, B. D. 2010. P-spline varying coefficient models for complex data. In: Tutz, G., and Kneib, T. (eds.), Statistical Modelling and Regression Structures, pp. 19–43 New York: Springer.Google Scholar
Marx, B. D. 2015. Varying-coefficient single-index signal regression. Chemometrics and Intelligent Laboratory Systems, 143, 111–121.Google Scholar
Marx, B. D., and Eilers, P. H. C. 1998. Direct generalized additive modeling with penalized likelihood. Computational Statistics and Data Analysis, 28, 193–209.Google Scholar
Marx, B. D., and Eilers, P. H. C. 1999. Generalized linear regression on sampled signals and curves: A P-spline approach. Technometrics, 41, 1–13.Google Scholar
Marx, B. D., and Eilers, P. H. C. 2005. Multidimensional penalized signal regression. Technometrics, 47, 13–22.Google Scholar
Marx, B. D., Eilers, P. H. C., Gampe, J., and Rau, R. 2010. Bilinear modulation models for seasonal tables of counts. Statistics and Computing, 20, 191–202.Google Scholar
Marx, B. D., Eilers, P. H. C., and Li, B. 2011. Multidimensional single-index signal regression. Chemometrics and Intelligent Laboratory Systems, 109, 120–130.Google Scholar
McCullagh, P., and Nelder, J. A. 1989. Generalized Linear Models, 2nd ed. London: Chapman and Hall.Google Scholar
Morris, J. S. 2015. Functional regression. Annual Review of Statistics and Its Application, 2, 321–359.Google Scholar
Newey, W., and Powell, J. L. 1987. Asymmetric least squares estimation and testing. Econometrica, 55, 819–647.CrossRefGoogle Scholar
Osborne, B. G., Fearn, T., Miller, A. R., and Douglas, S. 1984. Applications of near infrared reflectance spectroscopy to the compositional analysis of biscuits and biscuit dough. Journal of Scientific Food Agriculture, 35, 99–105.Google Scholar
O’Sullivan, F. 1986. A statistical perspective on ill-posed inverse problems (with discussion). Statistical Science, 1, 505–527.Google Scholar
Pandit, S. M., and Wu, S. M. 1993. Time Series and System Analysis with Applications. Malabar, FL: Krieger.Google Scholar
Pawitan, Y. 2001. In All Likelihood. Oxford: Oxford University Press.Google Scholar
Perperoglou, A., and Eilers, P. H. C. 2010. Penalized regression with individual deviance effects. Computational Statistics, 25, 341–361.Google Scholar
Portnoy, S., and Koenker, R. 1997. The Gaussian hare and the Laplacian tortoise: Computability of squared-error versus absolute-error estimators. Statistical Science, 12(4), 279–300.Google Scholar
Pya, N., and Wood, S. N. 2015. Shape constrained additive models. Statistics and Computing, 25, 543–559.Google Scholar
Ramsay, J. O., and Silverman, B. W. 2003. Functional Data Analysis, 2nd ed. New York: Springer.Google Scholar
Rigby, R. A., and Stasinopoulos, M.D. 2005. Generalized additive models for location, scale and shape. Journal of the Royal Computational Statistics & Applied Statistics, 54, 507–544.Google Scholar
Rigby, R. A., Stasinopoulos, M.D., Heller, G. Z., and De Bastiani, F. 2019. Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R. Boca Raton, FL: CRC Press.Google Scholar
Rippe, R. C. A., Meulman, J. J., and Eilers, P. H. C. 2012a. Reliable single chip genotyping with semi-parametric log-concave mixtures. PLoS ONE, 7(10): e46267.Google Scholar
Rippe, R. C. A., Meulman, J. J., and Eilers, P. H. C. 2012b. Visualization of genomic changes by segmented smoothing using an l0 penalty. PLoS ONE, 7(6): e38230.Google Scholar
Rizzi, S., Gampe, J., and Eilers, P. H. C. 2015. Efficient estimation of smooth distributions from coarsely grouped data. American Journal of Epidemiology, 182, 138–147.Google Scholar
Rizzi, S., Thinggaard, M., Engholm, G., Christensen, N., Johannesen, T. B., Vaupel, J. W., and Lindahl-Jacobsen, R. 2016. Comparison of non-parametric methods for ungrouping coarsely aggregated data. BMC Medical Research Methodology, 16(May 23).Google Scholar
Rodríguez-Alvarez, M. X., Boer, M. P., van Eeuwijk, F. A., and Eilers, P. H. C. 2018. Correcting for spatial heterogeneity in plant breeding experiments with P-splines. Spatial Statistics, 23, 52–71.Google Scholar
Rodríguez-Álvarez, M. X., Durbán, M., Lee, D.-J., and Eilers, P. H. C. 2019. On the estimation of variance parameters in non-standard generalised linear mixed models: Application to penalised smoothing. Statistics and Computing, 29(June), 483–500.Google Scholar
Rodríguez-Alvarez, M. X., Lee, D.-J., Kneib, T., Durbán, M., and Eilers, P. H. C. 2015. Fast smoothing parameter separation in multidimensional generalized P-splines: The SAP algorithm. Statistics and Computing, 25, 941–957.Google Scholar
Rue, H., Martino, S., and Chopin, N. 2009. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71, 319–392.Google Scholar
Ruppert, D. 2002. Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics, 11, 735–757.Google Scholar
Ruppert, D., and Carroll, R. J. 2000. Spatially-adaptive penalties for spline fitting. Australian & New Zealand Journal of Statistics, 42(2), 205–223.Google Scholar
Ruppert, D., Wand, M. P., and Carroll, R. J. 2003. Semiparametric Regression. Cambridge: Cambridge University Press.Google Scholar
Schall, R. 1991. Estimation in generalized linear models with random effects. Biometrika, 78, 719–727.Google Scholar
Schimek, M. G. 2009. Semiparametric penalized generalized additive models for environmental research and epidemiology. Environmetrics, 20, 699–717.Google Scholar
Schlattmann, P. 2009. Medical Applications of Finite Mixture Models. Berlin: Springer-Verlag.Google Scholar
Schlossmacher, E. J. 1973. An iterative technique for absolute deviations curve fitting. Journal of the American Statistical Association, 68(344), 857–859.Google Scholar
Schnabel, S. K., and Eilers, P. H. C. 2009. Optimal expectile smoothing. Computational Statistics & Data Analysis, 53, 4168–4177.Google Scholar
Schnabel, S. K., and Eilers, P. H. C. 2013a. A location-scale model for non-crossing expectile curves. Stat, 2(1), 171–183.Google Scholar
Schnabel, S. K., and Eilers, P. H. C. 2013b. Simultaneous estimation of quantile curves using quantile sheets. ASTA – Advances in Statistical Analysis, 97, 77–87.Google Scholar
Schoenberg, I. J. 1964. Spline functions and the problem of graduation. Proceedings of the American Mathematical Society, 52, 947–950.Google Scholar
Seber, G. A. F., and Lee, A. J. 2003. Linear Regression Analysis, 2nd ed. Hoboken, NJ: Wiley.Google Scholar
Selvin, S. 2019. The Joy of Statistics: A Treasury of Elementary Statistical Tools and their Applications. Oxford: Oxford University Press.Google Scholar
Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.Google Scholar
Stasinopoulos, M.D., and Rigby, R. A. 2007. Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23.Google Scholar
Stasinopoulos, M.D., Rigby, R. A., Heller, G. Z., Voudouris, V., and De Bastiani, F. 2017. Flexible Regression and Smoothing. Boca Raton, FL: Taylor & Francis Ltd.Google Scholar
Stone, M., and Brooks, R. J. 1990. Continuum regression: Cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal component regression. Journal of the Royal Statistical Society, Series B, 52, 237–269.Google Scholar
Thompson, R., and Baker, R. J. 1981. Composite link functions in generalized linear models. Applied Statistics, 30, 125–131.Google Scholar
Tibshirani, R. J., Saunders, M., Rosset, S., Zhu, J., and Knight, K. 2005. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society, Series B, 67, 9.Google Scholar
Umlauf, N., Adler, D., Kneib, T., Lang, S., and Zeileis, A. 2015. Structured additive regression models: An R interface to BayesX. Journal of Statistical Software, 63(21), 1–46.Google Scholar
van Buuren, S. 2007. Worm plot to diagnose fit in quantile regression. Statistical Modelling, 7(4), 363–376.Google Scholar
van Houwelingen, J. C., and Eilers, P. H. C. 2000. Non-proportional hazards models in survival analysis. In: Bethlehem, J. G. and van der Heijden, P. G. M. (eds.), COMPSTAT Proceedings in Computational Statistics 14th Symposium, pp. 151–160. New York: Springer.Google Scholar
Velazco, J. G., Rodríguez-Alvarez, X. M., Boer, M. P., Jordan, D. R., Eilers, P. H. C., Malosetti, M., and van Eeuwijk, F. A. 2017. Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model. Theoretical and Applied Genetics, 130, 1375–1392.Google Scholar
Verbeek, S., Eilers, P. H. C., Lawrence, K., Hennekam, R. C. M., and Versteegh, F. G. A. 2011. Growth charts for children with Ellis–van Creveld syndrome. European Journal of Pediatrics, 170, 207–211.Google Scholar
Verweij, P. J. M., and van Houwelingen, H. C. 1993. Cross-validation in survival analysis. Statistics in Medicine, 12, 2305–2314.Google Scholar
Waltrup, L. S., Sobotka, F., Kneib, T., and Kauermann, G. 2015. Expectile and quantile regression – David and Goliath? Statistical Modelling, 15(5), 433–456.Google Scholar
Wand, M. P., and Jones, M. C. 1995. Kernel Smoothing. London: Chapman and Hall.CrossRefGoogle Scholar
Wand, M. P., and Ormerod, J. T. 2008. On semiparametric regression with O’Sullivan penalized splines. Australian & New Zealand Journal of Statistics, 50, 179–198.Google Scholar
Wang, Y. 2011. Smoothing Splines: Methods and Applications. Boca Raton, FL: CRC Press.Google Scholar
Wang, Y., Yue, Y. R., and Faraway, J. J. 2018. Bayesian Regression Modeling with INLA. Boca Raton, FL: CRC Press.Google Scholar
Welham, S. J., Cullis, B. R., Kenward, M. G., and Thompson, R. 2006. The analysis of longitudinal data using mixed model L-splines. Biometrics, 62, 392–401.Google Scholar
Whittaker, E. T. 1923. On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63–75.Google Scholar
Wood, S. N. 2017. Generalized Additive Models: An Introduction with R, 2nd ed. Boca Raton, FL: CRC Press.Google Scholar
Wood, S. N., and Fasiolo, M. 2017. A generalized Fellner-Schall method for smoothing parameter optimization with application to Tweedie location, scale and shape models. Biometrics, 73, 1071–1081.Google Scholar
Xiao, L., Li, Y., and Ruppert, D. 2013. Fast bivariate P-splines: The sandwich smoother. Journal of the Royal Statistical Society, Series B, 75, 577–599.Google Scholar
Yavuz, A, C., and Lambert, P. 2016. Semi-parametric frailty model for clustered interval-censored data. Statistical Modelling, 16, 360–391.Google Scholar
Ye, J. 1998. On measuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association, 93, 120–131.Google Scholar
Yu, Y., and Ruppert, D. 2002. Penalized spline estimation for partially linear single-index models. Journal of the American Statistical Association, 97, 1042–1054.Google Scholar

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