A Robust Spectral Estimator With Application to a Noise-Corrupted Process

When a dataset is corrupted by noise, the model for data generating process is misspecified and can cause parameter-estimation problems. For example, in the case of a Gaussian autoregressive (AR) process corrupted by noise, data are more accurately modeled as an AR–moving-average process rather than an AR process. This misspecification leads to bias, and hence, low resolution in AR spectral estimation. However, a new parametric spectral estimator, the realizable information-theoretic estimator (RITE) based on a nonhomogeneous Poisson spectral representation, is shown by simulation to be more robust to white noise than the asymptotic maximum likelihood estimator (MLE). We, therefore, conducted an in-depth investigation and analyzed the statistics of RITE and the asymptotic MLE for the misspecified model. For large data records, both RITE and the asymptotic MLE are asymptotically normally distributed. The asymptotic MLE has a slightly lower variance, but RITE exhibits much less bias. Simulation examples of a white-noise-corrupted AR process are provided to support the theoretical properties. This advantage of RITE increases as the signal-to-noise-ratio decreases.