References
- Beresteanu , A. 2004 . “ ‘Nonparametric Estimation of Regression Functions Under Restrictions on Partial Derivatives’ ” . Duke University . Working paper 04-06
- Birke , M. and Dette , H. 2007 . Estimating a Convex Function in Nonparametric Regression . Scandinavian Journal of Statistics , 34 ( 2 ) : 384 – 404 . (doi:10.1111/j.1467-9469.2006.00534.x)
- Birke , M. and Dette , H. 2008 . A Note on Estimating a Monotone Regression Function by Combining Kernel and Density Estimates . Journal of Nonparametric Statistics , 20 ( 8 ) : 679 – 691 . (doi:10.1080/10485250802445399)
- Caroll , R. J. and Hall , P. 1988 . Optimal Rates of Convergence for Deconvolving a Density . Journal of the American Statistical Association , 83 ( 404 ) : 1184 – 1186 . (doi:10.1080/01621459.1988.10478718)
- Caroll , R. J. , Delaigle , A. and Hall , P. 2011 . Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement error . Journal of the American Statistical Association , 106 ( 493 ) : 191 – 202 . (doi:10.1198/jasa.2011.tm10355)
- Chmielewski , M. A. 1981 . Elliptically Symmetric Distributions: A Review and Bibliography . International Statistical Review , 49 ( 1 ) : 67 – 74 . (doi:10.2307/1403038)
- Delaigle , A. and Meister , A. 2007 . Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem . Journal of the American Statistical Association , 102 ( 480 ) : 1416 – 1426 . (doi:10.1198/016214507000000987)
- Dudley , R. M. 1984 . A Course on Empirical Processes. École d’Été de Probabilité de St. Flour XII , Vol. 1097 , 1 – 142 . Berlin, Heidelberg : Springer Verlag . Lecture Notes in Mathematics.
- Fan , J. and Truong , Y. K. 1993 . Nonparametric Regression with Errors in Variables . The Annals of Statistics , 21 ( 4 ) : 1900 – 1925 . (doi:10.1214/aos/1176349402)
- Frisen , M. 1986 . Unimodal Regression . The Statistician , 35 ( 4 ) : 479 – 485 . (doi:10.2307/2987804)
- Hildebrandt , T. H. and Schoenberg , I. J. 1933 . On Linear Functional Operations and the Moment Problem for a Finite Interval in One or Several Dimensions . Annals of Mathematics , 34 ( 2 ) : 317 – 328 . (doi:10.2307/1968205)
- Ioannides , A. D. and Alevizos , P. D. 1997 . Nonparametric Regression with Errors in Variables and Applications . Statistics & Probability Letters , 32 ( 1 ) : 35 – 43 . (doi:10.1016/S0167-7152(96)00054-5)
- Ioannides , D. A. and Matzner-Loeber , E. 2009 . Regression Quantiles with Errors-in-Variables . Journal of Nonparametric Statistics , 21 ( 8 ) : 1003 – 1015 . (doi:10.1080/10485250903019515)
- Kneip , A. and Engel , J. 1995 . Model Estimation in Nonlinear Regression Under Shape Invariance . The Annals of Statistics , 23 ( 2 ) : 551 – 570 . (doi:10.1214/aos/1176324535)
- Koushanfar , F. , Majzoobi , M. and Potkonjak , M. 2010 . Combinatorial Regression for Shape Constrained Modeling . IEEE Transactions on Signal Processing , 58 ( 2 ) : 626 – 637 . (doi:10.1109/TSP.2009.2028937)
- Kulikov , V. N. and Lopuhaa , H. P. 2006 . The Behavior of the NPMLE of a Deceasing Density Near the Boundaries of the Support . The Annals of Statistics , 34 ( 2 ) : 742 – 768 . (doi:10.1214/009053606000000100)
- Mammen , E. 1991 . Nonparametric Regression Under Qualitative Smoothness Assumptions . The Annals of Statistics , 19 ( 2 ) : 741 – 759 . (doi:10.1214/aos/1176348118)
- Meister , A. 2009 . Deconvolution Problems in Nonparametric Statistics , Vol. 193 , Berlin, Heidelberg : Springer Verlag . Lecture Notes in Statistics.
- Meyer , M. C. 2008 . Inference Using Shape-Restricted Regression Splines . Annals of Applied Statistics , 2 ( 3 ) : 1013 – 1033 . (doi:10.1214/08-AOAS167)
- Rockafellar , R. T. and Wets , R. J.-B. 2009 . Variational Analysis , Berlin/Heidelberg/New York : Springer, Verlag . (Vol. 317, 3rd printing), Grundlehren der Mathematischen Wissenschaften
- Ryan , S. and Wets , R. J.-B. 2013 . Energy-Loads Forecasting . Techn. , Report, UC Davis.
- Schennach , S. M. 2004 . Nonparametric Regression in the Presence of Measurement Errors . Econometric Theory , 20 ( 6 ) : 1046 – 1093 . (doi:10.1017/S0266466604206028)
- Stefanski , L. and Caroll , R. J. 1990 . Deconvolution Kernel Density Estimators . Statistics , 21 : 169 – 184 . (doi:10.1080/02331889008802238)
- Wang , J. and Gosh , S. K. 2012 . Shape Restricted Nonparametric Regression with Bernstein Polynomials . Computational Statistics and Data Analysis , 56 ( 9 ) : 2729 – 2741 . (doi:10.1016/j.csda.2012.02.018)
- Zwanzig , S. 1999 . How to Adjust Nonparametric Regression Estimators to Models with Errors in the Variables . Theory of Stochastic Processes , 5 ( 21 ) : 272 – 277 .