Bayes Least Squares Linear Regression is Asympotically Full Bayes: Estimation of Spectral Densities

摘要

Bayes least squares linear (BLSL) estimators were introduced by Whittle and described explicitly and further developed by Hartigan. The method was applied to estimation of coefficients of orthogonal expansions of regression functions in another work. In this present paper it is noted that when many observations are available the BLSL method can be expected to yield substantially the same results as a full Bayesian treatment; and the method is illustrated in the context of estimation of spectral densities. In that context, the estimators suggested will appear rather ordinary. But they are not completely ad hoc: each comes with an interpretation. And, when large samples are available, the posterior distribution of the estimator at a fixed frequency is (approximately) normal, with easily calculated standard deviation.