Response of the ordinary least squares estimator (OLS) to deterministic and stochastic noise

摘要

Mapping functions and OPDFs (optimum parameter driving functions) defined in this paper are simple, intuitive, and useful tools for evaluating OLS parameter estimates. Parameter errors equal the inner product of the noise waveform and the mapping functions. Low orthogonality of the sensitivities (regressors) increases the mapping functions and the error of each parameter by a factor equal to its GDOP (geometric dilution of precision). The smallest signals able to produce unit parameter changes are the OPDFs. Spectral analysis of the mapping functions exposes the spectral sensitivity of a parameter to added noise.