Linear estimation for discrete systems with uncertain observations: an application to the correction of declared incomes in inquiry
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.
scientific article; zbMATH DE number 2116561