2015 •
Orthogonal Series Estimation of Regression Functions in Nonstationary Conditions
Authors:
Tomasz Galkowski, Miroslaw Pawlak
Abstract:
The article concerns of the problem of regression functions estimation when the output is contaminated by additive nonstationary noise. We investigate the model \(y_i = R\left( {{\bf x _i}} \right) + Z _i ,\,i = 1,2, \ldots n\), where x i is assumed to be the set of deterministic inputs (d-dimensional vector), y i is the scalar, probabilistic outputs, and Z i is a measurement noise with zero mean and variance depending on n. \(R\left( . \right)\) is a completely unknown function. The problem of finding function \(R\left( . \right)\) may be solv (...)
The article concerns of the problem of regression functions estimation when the output is contaminated by additive nonstationary noise. We investigate the model \(y_i = R\left( {{\bf x _i}} \right) + Z _i ,\,i = 1,2, \ldots n\), where x i is assumed to be the set of deterministic inputs (d-dimensional vector), y i is the scalar, probabilistic outputs, and Z i is a measurement noise with zero mean and variance depending on n. \(R\left( . \right)\) is a completely unknown function. The problem of finding function \(R\left( . \right)\) may be solved by applying non-parametric methodology, for instance: algorithms based on the Parzen kernel or algorithms derived from orthogonal series. In this work we present the orthogonal series approach. The analysis has been made for some class of nonstationarity. We present the conditions of convergence of the estimation algorithm for the variance of noise growing up when number of observations is tending to infinity. The results of numerical simulations are presented. (Read More)
We have placed cookies on your device to help make this website and the services we offer better. By using this site, you agree to the use of cookies. Learn more