The Annals of Statistics
- Ann. Statist.
- Volume 13, Number 4 (1985), 1286-1316.
Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions
The likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions. This approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations. It is then shown that this method is equivalent to placing a diffuse prior distribution on the unspecified part of the initial state vector, and modified versions of the Kalman filter and smoothing algorithms are derived to give exact numerical procedures for diffuse initial conditions. The results are extended to continuous time models, including smoothing splines and continuous time autoregressive processes.
Ann. Statist., Volume 13, Number 4 (1985), 1286-1316.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M15: Spectral analysis
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Ansley, Craig F.; Kohn, Robert. Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions. Ann. Statist. 13 (1985), no. 4, 1286--1316. doi:10.1214/aos/1176349739. https://projecteuclid.org/euclid.aos/1176349739