Estimation of heteroscedastic measurement noise variances

For any quantitative data interpretation it is crucial to have information about the noise variances. Unfortunately, this information is often unavailable a priori. We propose a procedure to estimate the noise variances starting from the residuals. The method takes two difficulties into account. (i) The noise can be heteroscedastic (not constant over the measurement domain). This implies that one number is not enough anymore to characterise the total noise variance structure. (ii) The initial model used to generate the residuals may be imperfect. As a consequence, the residuals contain more than only stochastic information. The outcome of our procedure is an estimate of the noise variances which depends on the sample number, but is independent of the postulated model. A by-product of the procedure is information about the distribution of the degrees of freedom over the measurement domain. Indeed, as a consequence of the heteroscedastic noise, the model parameters will be fitted more to those data with low uncertainty and most of the degrees of freedom are lost at these locations. (c) 2006 Elsevier B.V. All rights reserved.