Strong Nonlinear Correlations, Conditional Entropy and Perfect Estimation
Christopher S. Jones, John M. Finn, Nicolas Hengartner, Kevin H. Knuth, Ariel Caticha, Adom Giffin, Carlos C. Rodríguez · AIP conference proceedings · 2007
This paper deals with parameter estimation in which measurements subjected to highly correlated noise allow for very accurate estimation. For linear regression with normally distributed noise, this generically occurs when the noise becomes highly linearly correlated. For a linear model with nonnormal noise distributions, there may exist nonlinear regressions that allow for accurate estimation if a conditional entropy is small (analogous to linear correlations in the normal case approaching ±1.) Nonlinear regression may also yield an accurate estimate if a nonlinear model is subjected to strongly linearly correlated noise.