Extensions to the invariance property of maximum likelihood estimation for affine-transformed state-space models

Replacing the state vector of a linear state-space model by any one-to-one linear transformation does not alter maximum likelihood estimation. We extend this invariance property to more general settings, with possibly diffuse initialization of the Kalman filter and injective affine transformations of the state vector. Our results hold for both direct maximization of the likelihood function and the EM algorithm. We offer two real examples that illustrate how one may employ our results to handle a variety of affine-transformed state-space models in the literature. (AU)