On Convergence Rates of Convex Regression in Multiple Dimensions

被引：13
作者：
Lim, Eunji [1 ]
机构：
[1] Kean Univ, Dept Management Mkt & Int Business, Union, NJ 07083 USA
来源：
INFORMS JOURNAL ON COMPUTING | 2014年 / 26卷 / 03期
关键词：
nonparametric regression; multidimensional convex functions; convergence rates; asymptotic properties; CONSISTENCY;
D O I：
10.1287/ijoc.2013.0587
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We consider a least squares estimator for estimating a convex function f(*): [0,1](d) -> R with bounded su-gradients. A rate at which the sum of squared differences between the estimator and the true function f(*) converges to zero is computed. This work sheds light on computing the convergence rate of the multidimenstional convex regression estimator.
引用
收藏
页码：616 / 628
页数：13
相关论文
共 30 条
  • [1] Nonparametric estimation of concave production technologies by entropic methods
    Allon, Gad
    Beenstock, Michael
    Hackman, Steven
    Passy, Ury
    Shapiro, Alexander
    [J]. JOURNAL OF APPLIED ECONOMETRICS, 2007, 22 (04) : 795 - 816
  • [2] [Anonymous], 2013, Introductory lectures on convex optimization: A basic course
  • [3] [Anonymous], 2007, Stochastic Simulation: Algorithms and Analysis
  • [4] [Anonymous], 2014, INFORMS J COMPUTING, V26, P616
  • [5] BRONSHTEIN EM, 1976, SIBERIAN MATH J+, V17, P393
  • [6] ROBUST LOCALLY WEIGHTED REGRESSION AND SMOOTHING SCATTERPLOTS
    CLEVELAND, WS
    [J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1979, 74 (368) : 829 - 836
  • [7] Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
    Cule, Madeleine
    Samworth, Richard
    [J]. ELECTRONIC JOURNAL OF STATISTICS, 2010, 4 : 254 - 270
  • [8] APPROXIMATION BY LOG-CONCAVE DISTRIBUTIONS, WITH APPLICATIONS TO REGRESSION
    Duembgen, Lutz
    Samworth, Richard
    Schuhmacher, Dominic
    [J]. ANNALS OF STATISTICS, 2011, 39 (02) : 702 - 730
  • [9] Groeneboom P, 2001, ANN STAT, V29, P1653
  • [10] Hall P, 2001, ANN STAT, V29, P624
123