Linear estimation for discrete systems with uncertain observations: an application to the correction of declared incomes in inquiry
type: Item
instance of: scholarly article
title: Linear estimation for discrete systems with uncertain observations: an application to the correction of declared incomes in inquiry
zbMATH Open document ID: 1061.65057
published in: Applied Mathematics and Computation
publication date: 2004-11-18T00:00:00Z
review text: This paper is built within two main stages: (a) In the first phase, the aim of the paper is to derive a new algorithm for estimating the state of discrete systems with uncertain observations in which the state and measurement noises are correlated on a finite interval time. Making use of the orthogonal projection technique, the authors obtain a recursive algorithm for the least mean squared error linear filtering and prediction problems. (b) In the second phase, the new estimation algorithm is applied in the economic field to the problem of correcting the distribution of the personal declared incomes deduced from inquiries. Specifically, the declared incomes obtained through inquiry are corrected using a state space model with uncertain observations. The relationship between hidden, declared, and real incomes of n families belonging to an autonomous community is expressed in terms of this state space model. The important hypotheses which the financial modelling is based on are that (1) the hidden personal incomes are proportional to the real ones, and (2) all of the families hide their incomes to a certain extent or, equivalently, that some families do not hide their income. Two Mathematica code programs have implemented the proposed correction method, and the obtained results have been compared with the real information from (Spain) regional accounting and with previous computational methods. The work shows a better estimation of the proposed technique and, essentially, its improved behaviour as the occultation rate grows.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 91B82
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93E24
zbMATH DE Number: 2116561
zbMATH Keywords: Kalman filtering
zbMATH Keywords: estimation algorithm
zbMATH Keywords: family income estimations
zbMATH Keywords: hidden income estimation
zbMATH Keywords: uncertain observations
zbMATH Keywords: least mean squar error
zbMATH Keywords: linear filtering
zbMATH Keywords: income inquiry
zbMATH Keywords: finance
zbMATH Keywords: discrete systems
zbMATH Keywords: prediction
zbMATH Keywords: Mathematica code programs
zbMATH Keywords: correction method
author: C. Sánchez-González
author: T. M. García-Muñoz
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: j.amc.2003.07.029
OpenAlex ID: W1997736563
cites work: Stochastic processes and filtering theory
cites work: Q5632433
cites work: Q5623579
cites work: Filtering in discrete-time systems with state and observation noises correlated on a finite time interval
cites work: Optimal recursive estimation with uncertain observation
cites work: Linear estimation for discrete-time systems in the presence of time-correlated disturbances and uncertain observations
cites work: Q4039873
DOI: 10.1016/J.AMC.2003.07.029
description: scientific article; zbMATH DE number 2116561