@article{oai:sucra.repo.nii.ac.jp:00015045,
 author = {丸茂, 幸平 and WOLFF, Rodney},
 issue = {8},
 journal = {Working Paper Series},
 month = {Mar},
 note = {We discuss the use of the orthogonal expansions for the approximation of probability density functions under constraints. For given independent and identically distributed samples, it has been shown by Marumo and Wolff (2013) that smooth functions that approximate the empirical distribution function can be constructed using orthogonal polynomial expansion. The approximation of the density function is given as the derivative of this smooth function.
In this paper, we show that the approximations under constraints on the moments and risk measures such as Value at Risk and Expected Shortfall can be constructed using orthogonal expansions.
The biggest advantage of our method over the typical existing methods is that our method has an explicit formula for the constrained approximations, whereas others often require intensive numerical calculations., text, application/pdf},
 pages = {1--19},
 title = {Density Approximation with Orthogonal Expansions Under Constraints},
 year = {2015},
 yomi = {マルモ, コウヘイ}
}