An Application of Isotonic Regression to Multivariate Density Estimation

1986 ◽  
pp. 69-90 ◽  
Author(s):  
Thomas W. Sager
Keyword(s):  
Density Estimation ◽  
Isotonic Regression ◽  
Multivariate Density Estimation ◽  
Multivariate Density

Box-spline histograms for multivariate density estimation

2010 ◽  
Vol 37 (4) ◽  
pp. 413-427
Author(s):  
Karol Dziedziul ◽  
Piotr Paluszek
Keyword(s):  
Density Estimation ◽  
Multivariate Density Estimation ◽  
Box Spline ◽  
Multivariate Density

Nonparametric multivariate density estimation: a comparative study

1994 ◽  
Vol 42 (10) ◽  
pp. 2795-2810 ◽  
Author(s):  
Jenq-Neng Hwang ◽  
Shyh-Rong Lay ◽  
A. Lippman
Keyword(s):  
Comparative Study ◽  
Density Estimation ◽  
Multivariate Density Estimation ◽  
Multivariate Density

A note on wavelet deconvolution density estimation

2017 ◽  
Vol 15 (06) ◽  
pp. 1750055 ◽  
Author(s):  
Xiaochen Zeng
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Density Estimation ◽  
Besov Spaces ◽  
One Dimensional ◽  
Bounded Set ◽  
Multivariate Density Estimation ◽  
Free Case ◽  
Ill Posed ◽  
Multivariate Density

This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Giné and Nickl’s (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry’s theorem (Stoch. Process. Appl., 1997) to some extent.

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