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Applications and Case Studies

A Marginal Approach to Reduced-Rank Penalized Spline Smoothing With Application to Multilevel Functional Data

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Pages 1216-1229 | Received 01 Jan 2012, Published online: 19 Dec 2013

REFERENCES

  • Apanasovich , T. , Ruppert , D. , Lupton , J. , Popovic , N. , Turner , N. , Chapkin , R. and Carrol , R. 2008 . Aberrant Crypt Foci and Semiparametric Modeling of Correlated Binary Data . Biometrics , 64 : 490 – 500 .
  • Baladandayuthapani , V. , Mallick , B. , Turner , N. , Hong , M. , Chapkin , R. , Lupton , J. and Carroll , R. J. 2008 . Bayesian Hierarchical Spatially Correlated Functional Data Analysis With Application to Colon Carcinogenesis . Biometrics , 64 : 64 – 73 .
  • Brumback , B. and Rice , J. 1998 . “Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves” (with discussion) . Journal of the American Statistical Association , 93 : 961 – 994 .
  • Choi , H. A. , Ko , S. B. , Chen , H. , Gilmore , E. , Carpenter , A. M. , Lee , D. , Claassen , J. , Mayer , S. A. , Schmidt , J. M. , Lee , K. , Connelly , E. S. , Paik , M. and Badjatia , N. 2012 . Acute Effects of Nimodipine on Cerebral Vasculature and Brain Metabolism in High Grade Subarachnoid Hemorrhage Patients . Neurocritical Care , 16 : 363 – 367 .
  • Claeskens , G. , Krivobokova , T. and Opsomer , J. D. 2009 . Asymptotic Properties of Penalized Spline Estimators . Biometrika , 96 : 529 – 544 .
  • Crainiceanu , C. M. , Staicu , A. M. and Di , C. 2009 . Generalized Multilevel Functional Regression . Journal of the American Statistical Association , 104 : 1550 – 1561 .
  • Crainiceanu , C. M. , Staicu , A. M. , Ray , S. and Punjabi , N. 2012 . Bootstrap-Based Inference on the Difference in the Means of Two Correlated Functional Processes . Statistics and Medicine , 31 : 3223 – 3240 .
  • Craven , P. and Wahba , G. 1979 . Smoothing Noisy Data With Spline Functions: Estimating the Correct Degree of Smoothing by the Methods of Generalized Cross-Validation . Numerische Mathematik , 31 : 377 – 403 .
  • Di , C. , Crainiceanu , C. M. , Caffo , B. S. and Punjabi , N. M. 2009 . Multilevel Functional Principal Component Analysis . Annals of Applied Statistics , 3 : 458 – 488 .
  • Diggle , P. J. , Liang , K. Y. and Zeger , S. L. 2002 . Analysis of Longitudinal Data (2nd ed.) , Oxford : Oxford University Press .
  • Diringer , M. N. , Bleck , T. P. , Claude , H. J. , Menon , D. , Shutter , L. , Vespa , P. , Bruder , N. , Connolly , E. S. , Citerio , G. , Gress , D. , Hanggi , D. , Hoh , B. L. , Lanzino , G. , Le , R. P. , Rabinstein , A. , Schmutzhard , E. , Stocchetti , N. , Suarez , J. I. , Treggiari , M. , Tseng , M. Y. , Vergouwen , M. D. , Wolf , S. , Zipfel , G. and Neurocritical Care Society . 2011 . Critical Care Management of Patients Following Aneurysmal Subarachnoid Hemorrhage: Recommendations From the Neurocritical Care Society's Multidisciplinary Consensus Conference . Neurocritical Care , 15 : 211 – 240 .
  • Dorhout , S. M. , Rinkel , G. J. , Feigin , V. L. , Algra , A. , van den Bergh , W. M. , Vermeulen , M. and van Gijn , J. 2007 . Calcium Antagonists for Aneurysmal Subarachnoid Haemorrhage . Cochrane Database System Review , 18 : CD000277
  • Eilers , P. and Marx , B. 1996 . Flexible Smoothing With B-Splines . Statistical Science , 11 : 89 – 121 .
  • Fan , J. 1992 . Design-Adaptive Nonparametric Regression . Journal of the American Statistical Association , 87 : 998 – 1004 .
  • Fu , W. 2003 . Penalized Estimating Equations . Biometrics , 59 : 126 – 132 .
  • Goldsmith , J. , Greven , S. and Crainiceanu , C. 2013 . Corrected Confidence Bands for Functional Data Using Principal Components . Biometrics , 69 : 41 – 51 .
  • Guo , W. 2002 . Functional Mixed Effects Models . Biometrics , 58 : 121 – 128 .
  • Ibrahim , A. and Suliadi , S. 2010a . GEE-Smoothing Spline in Semiparametric Model With Correlated Nominal Data: Estimation and Simulation Study . ASM’10 Proceedings of the 4th International Conference on Applied Mathematics, Simulation, Modelling , : 19 – 26 .
  • Ibrahim , A. and Suliadi , S. 2010b . Analyzing Longitudinal Data Using Gee-Smoothing Spline . Proceedings of the 8th WSEAS International Conference on Applied Computer and Applied Computational Science , : 26 – 33 .
  • Jaeger , M. , Schuhmann , M. U. , Soehle , M. and Meixensberger , J. 2006 . Continuous Assessment of Cerebrovascular Autoregulation After Traumatic Brain Injury Using Brain Tissue Oxygen Pressure Reactivity . Critical Care Medicine , 34 : 1783 – 1788 .
  • Krivobokova , T. , Kneib , T. and Claeskens , G. 2010 . Simultaneous Confidence Bands for Penalized Spline Estimators . Journal of the American Statistical Association , 105 : 852 – 863 .
  • Li , Y. and Ruppert , D. 2008 . On the Asymptotics of Penalized Splines . Biometrika , 95 : 415 – 436 .
  • Lin , X. and Carroll , R. 2000 . Nonparametric Function Estimation for Clusterted Data When the Predictor is Measured Without/With Error . Journal of the American Statistical Association , 95 : 520 – 534 .
  • Lin , X. , Wang , N. , Welsh , A. and Carroll , R. 2004 . Equivalent Kernels of Smoothing Splines in Nonparametric Regression for Clustered Data . Biometrika , 92 : 177 – 193 .
  • Marra , G. and Wood , S. N. 2012 . Coverage Properties of Confidence Intervals for Generalized Additive Model Components . Scandinavian Journal of Statistics , 39 : 53 – 74 .
  • Opsomer , J. D. , Wang , Y. and Yang , Y. 2001 . Nonparametric Regression With Correlated Errors . Statistical Science , 16 : 134 – 153 .
  • Rice , J. and Wu , C. 2001 . Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves . Biometrics , 57 : 253 – 259 .
  • Ruppert , D. 2002 . Selecting the Number of Knots for Penalized Splines . Journal of Computational and Graphical Statistics , 11 : 735 – 757 .
  • Ruppert , D. , Wand , M. P. and Carroll , R. J. 2003 . Semiparametric Regression , New York : Cambridge University Press .
  • Staicu , A. , Crainiceanu , C. and Carroll , C. 2010 . Fast Methods for Spatially Correlated Multilevel Functional Data . Biostatistics , 11 : 177 – 194 .
  • Stiefel , M. F. , Heuer , G. G. , Abrahams , J. M. , Bloom , S. , Smith , M. J. , Maloney-Wilensky , E. , Grady , M. S. and LeRoux , P. D. 2004 . The Effect of Nimodipine on Cerebral Oxygenation in Patients With Poor-Grade Subarachnoid Hemorrhage . Journal of Neurosurgery , 101 : 594 – 599 .
  • Wahba , G. 1985 . A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem . The Annals of Statistics , 4 : 1378 – 1402 .
  • Wand , M. P. 2003 . Smoothing and Mixed Models . Computational Statistics , 18 : 223 – 249 .
  • Wang , N. 2003 . Marginal Nonparametric Kernel Regression Accounting for Within-Subject Correlation . Biometrika , 90 : 43 – 52 .
  • Wang , Y. and Chen , H. 2012 . “On Testing an Unspecified Function Through a Linear Mixed Effects Model With Multiple Variance Components,” . Biometrics , 68 : 1113 – 1125 .
  • Wang , Z. and Louise , T. 2003 . Matching Conditional and Marginal Shapes in Binary Random Intercept Models Using a Bridge Distribution Function . Biometrika , 90 : 765 – 775 .
  • Welsh , A. , Lin , X. and Carroll , R. 2002 . Marginal Longitudinal Nonparametric Regression: Locality and Efficiency of Spline and Kernel Methods . Journal of the American Statistical Association , 97 : 482 – 493 .
  • Wood , S. N. 2011 . Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models . Journal of the Royal Statistical Society, Series B , 73 : 3 – 36 .
  • Wu , H. and Zhang , J. 2006 . Nonparametric Regression Methods for Longitudinal Data Analysis Mixed-Effects Modeling Approaches , Hoboken, , NJ : Wiley .
  • Zhao , L. P. , Prentice , R. and Self , S. 1992 . Multivariate Mean Parameter Estimation by Using a Partly Exponential Model . Journal of the Royal Statistical Society, Series B , 54 : 805 – 811 .
  • Zhou , L. , Huang , J. and Carroll , R. 2008 . Joint Modeling of Paired Sparse Functional Data Using Principal Components . Biometrika , 95 : 601 – 619 .
  • Zhu , Z. , Fung , W. K. and He , X. 2008 . On the Asymptotics of Marginal Regression Splines With Longitudinal Data . Biometrika , 95 : 907 – 917 .

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