On the moment-recovered approximations of regression and derivative functions with applications

In this paper three formulas for recovering the conditional mean and conditional variance based on product moments are proposed. The upper bounds for the uniform rate of approximations of regression and derivatives of some moment-determinate function are derived. Two cases where the support of underlying functions is bounded and unbounded from above are studied. Based on the proposed approximations, novel nonparametric estimates of the distribution function and its density in multiplicative-censoring model are constructed. Simulation study justifies the consistency of the estimates.

[1]  C. Chesneau,et al.  MULTIPLICATIVE CENSORING: ESTIMATION OF A DENSITY AND ITS DERIVATIVES UNDER THE Lp-RISK , 2013 .

[2]  Cleve Moler,et al.  Mathematical Handbook for Scientists and Engineers , 1961 .

[3]  Robert M. Mnatsakanov,et al.  Hausdorff moment problem: Reconstruction of probability density functions , 2008 .

[4]  Christian Kleiber,et al.  Multivariate distributions and the moment problem , 2013, J. Multivar. Anal..

[5]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[6]  Aldo Tagliani,et al.  Hamburger moment problem and Maximum Entropy: On the existence conditions , 2014, Appl. Math. Comput..

[7]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[8]  Aldo Tagliani,et al.  Stieltjes moment problem via fractional moments , 2005, Appl. Math. Comput..

[9]  R. Mnatsakanov.  Recovery of functions from transformed moments: A unified approach , 2017 .

[10]  John van der Hoek,et al.  CONDITIONAL EXPECTATION FORMULAE FOR COPULAS , 2008 .

[11]  Gwo Dong Lin,et al.  On the moment problems , 1997 .

[12]  Charles Hagwood,et al.  Reconstruction of conditional expectations from product moments with applications , 2015, J. Comput. Appl. Math..

[13]  J. Shohat,et al.  The problem of moments , 1943 .

[14]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[15]  Henryk Gzyl,et al.  Stieltjes moment problem and fractional moments , 2010, Appl. Math. Comput..

[16]  Aldo Tagliani.  Hausdorff moment problem and fractional moments: A simplified procedure , 2011, Appl. Math. Comput..

[17]  Serge B. Provost,et al.  A Viable Alternative to Resorting to Statistical Tables , 2007, Commun. Stat. Simul. Comput..

[18]  Robert M. Mnatsakanov,et al.  Moment-recovered approximations of multivariate distributions: The Laplace transform inversion , 2011 .

[19]  Å. Björck,et al.  Solution of Vandermonde Systems of Equations , 1970 .

[20]  R. Mnatsakanov.  Hausdorff moment problem: Reconstruction of distributions , 2008 .