Nearly-isotonic regression

Technometrics

Volumn 53, Issue 1, 2011, Pages 54-61

  Tibshirani, Ryan J ^a   Hoefling, Holger ^b   Tibshirani, Robert ^a  

^a STANFORD UNIVERSITY   (United States)

^b NOVARTIS PHARMA AG   (Switzerland)

Author keywords

Degrees of freedom; Isotonic regression; Path algorithm; Pool adjacent violators

Indexed keywords

CONVEX OPTIMIZATION PROBLEMS; DATA POINTS; DEGREES OF FREEDOM; ISOTONIC REGRESSION; MONOTONE FUNCTIONS; MONOTONICITY; NUMBER OF DATUM; PATH ALGORITHM; POOL ADJACENT VIOLATORS; SIMPLE ALGORITHM; UNBIASED ESTIMATES;

ALGORITHMS; CONVEX OPTIMIZATION; LAKES; MECHANICS;

REGRESSION ANALYSIS;

EID: 79251592855     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/TECH.2010.10111     Document Type: Article

References (21)

1. Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T., and Silverman, E. (1955), "An Empirical Distribution Function for Sampling With Incomplete Information," Annals of Mathematical Statistics, 26 (4), 641-647. [54]
2. Barlow, R. E., Bartholomew, D., Bremner, J. M., and Brunk, H. D. (1972), Statistical Inference Under Order Restrictions: The Theory and Application of Isotonic Regression, New York: Wiley. [54]
3. Bartholomew, D. J. (1959a), "A Test for Homogeneity for Ordered Alternatives," Biometrika, 46 (1), 36-48. [54]
4. - (1959b), "A Test for Homogeneity for Ordered Alternatives II," Biometrika, 46 (3), 328-335. [54]
5. Brunk, H. D. (1955), "Maximum Likelihood Estimates of Monotone Parameters," Annals of Mathematical Statistics, 26 (4), 607-616. [54]
6. de Leeuw, J., Hornik, K., and Mair, P. (2009), "Isotone Optimization in R: Pool-Adjacent-Violators (PAVA) and Active Set Methods," Journal of Statistical Software, 32 (5), 1-24. [54]
7. Efron, B. (1986), "How Biased Is the Apparent Error Rate of a Prediction Rule?" Journal of the American Statistical Association, 81 (394), 461-470. [56]
8. Evans, L., and Gariepy, R. (1992), Measure Theory and Fine Properties of Functions, Boca Raton, FL: CRC Press. [60]
9. Friedman, J., Hastie, T., Hoefling, H., and Tibshirani, R. (2007), "Pathwise Coordinate Optimization," The Annals of Applied Statistics, 1 (2), 302-332. [55,59]
10. Grotzinger, S. J., and Witzgall, C. (1984), "Projections Onto Simplices," Applied Mathematics and Optimization, 12 (1), 247-270. [54]
11. Hastie, T., Tibshirani, R., and Friedman, J. (2008), The Elements of Statistical Learning: Data Mining, Inference and Prediction (2nd ed.), New York: Springer-Verlag. [56]
12. Hoefling, H. (2010), "A Path Algorithm for the Fused Lasso Signal Approximator," unpublished manuscript, University of Freiburg, available at http://www.holgerhoefling.com/Articles/FusedLasso.pdf. [55,56,58]
13. Luss, R., Rosset, S., and Shahar, M. (2010), "Isotonic Recursive Partioning," unpublished manuscript, Tel Aviv University. [54,56,59]
14. Meyer, M., and Woodroofe, M. (2000), "On the Degrees of Freedom in Shape-Restricted Regression," The Annals of Statistics, 28 (4), 1083-1104. [56,60]
15. Miles, R. E. (1959), "The Complete Amalgamation Into Blocks, by Weighted Means, of a Finite Set of Real Numbers," Biometrika, 46 (3), 317-327. [54]
16. R Development Core Team (2008), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing. Available at http://www.R-project.org. [59]
17. Robertson, T., Wright, F. T., and Dykstra, R. L. (1988), Order Restricted Statistical Inference, New York: Wiley. [54]
18. Schlegel, P. (1970), "The Explicit Inverse of a Tridiagonal Matrix," Mathematics of Computation, 24 (111), 665-665. [59]
19. Stein, C. (1981), "Estimation of the Mean of a Multivariate Normal Distribution," The Annals of Statistics, 9 (6), 1135-1151. [59]
20. Tibshirani, R., and Taylor, J. (2010), "The Solution Path of the Generalized Lasso," unpublished manuscript, Stanford University, available at http://www-stat.stanford.edu/~ryantibs/papers/genlasso.pdf. [60]
21. Wu, W., Woodroofe, M., and Mentz, G. (2001), "Isotonic Regression: Another Look at the Changepoint Problem," Biometrika, 88 (3), 794-804. [57]