A comparison between robust information theoretic estimator and asymptotic maximum likelihood estimator for misspecified model

A robust information-theoretic estimator (RITE) is based on a non-homogeneous Poisson spectral representation. When an autoregressive (AR) Gaussian wide sense stationary (WSS) process is corrupted by noise, RITE is analyzed and shown by simulation to be more robust to noise than the asymptotic maximum likelihood estimator (MLE). The statistics of RITE and asymptotic MLE are analyzed for the misspecified model. For large data records, RITE and MLE are asymptotically normally distributed. MLE has lower variance, but RITE exhibits much less bias. Simulation examples of a noise corrupted AR process are provided to support the theoretical properties and show the advantage of RITE for low signal-to-noise ratios (SNR)