Paper Info
Title
A two-dimensional Poisson equation formulation of non-parametric statistical non-linear modeling
Abstract
The present paper deals with a Poisson equation arising in statistical modeling of semi-deterministic non-linear systems with two independent (input) variables and one dependent (output) variable. Statistical modeling is formulated in terms of a differential equation that relates the second-order joint probability density functions of the model's input/output random variables with the sought non-linear model transference. The discussed modeling procedure makes no prior assumptions on the functional structure of the model, except for monotonicity and continuity with respect to both input variables. In particular, the method is non-parametric. Results of numerical tests are presented and discussed in order to get an insight into the behavior of the devised statistical modeling procedure. The results of numerical tests confirm that the proposed statistical modeling approach is able to cope with both synthetic and real-world data sets and, in particular, with underlying systems and data that exhibit strong hidden nuisance variables and measurement disturbances.
Year
DOI
Venue
2014
10.1016/j.camwa.2013.12.002
Computers & Mathematics with Applications
Keywords
Field
DocType
proposed statistical modeling approach,differential equation,numerical test,statistical modeling,input variable,poisson equation,statistical modeling procedure,real-world data set,non-linear model transference,two-dimensional poisson equation formulation,output random variable,non-parametric statistical non-linear modeling
Differential equation,Random variable,Mathematical optimization,Joint probability distribution,Poisson's equation,Structural equation modeling,Mathematical analysis,Nuisance variable,Nonparametric statistics,Statistical model,Mathematics
Journal
Volume
Issue
ISSN
67
5
0898-1221
Citations 
PageRank 
References 
0
0.34
8
Authors
1
Name
Order
Citations
PageRank
Simone Fiori149452.86